共查询到20条相似文献,搜索用时 31 毫秒
1.
E. Brézin C. De Dominicis 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(1):71-76
The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension
six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking
of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends
of the system in order to study the size dependence of the twist free energy. A loop-expansion is performed to first order
around a twisted background. It is found, as expected but it is non trivial, that the theory does renormalize around such
backgrounds, as well as for the bulk. However two main differences appear, in comparison with simple ferromagnetic transitions:
(i) the loop expansion yields a (negative) anomaly in the size dependence of the free energy, thereby lifting the lower critical
dimension to a value greater than two (ii) the free energy is lowered by twisting the boundary conditions. This situation
is common in spin glasses, reflecting the non-positivity of mode multiplicity in replica symmetry breaking, but its physical
meaning is still unclear.
Received 12 April 2002 / Received in final form 30 July 2002 Published online 19 November 2002 相似文献
2.
G. Parisi F. Tria 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(4):533-541
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington
Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry
breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average
connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient
of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this
annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the
temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry
breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking.
The 1/z expansion is well defined also in the zero temperature limit.
Received 15 July 2002 Published online 31 December 2002 相似文献
3.
G. Parisi F. Slanina 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(4):603-611
We present a variational approach for directed polymers in D transversal dimensions which is used to compute the correction to the mean field theory predictions with broken replica symmetry.
The trial function is taken to be a symmetrized version of the mean-field solution, which is known to be exact for . We compute the free energy corresponding to that function and show that the finite-D corrections behave like D
-4/3
. It means that the expansion in powers of 1/D should be used with great care here. We hope that the techniques developed in this note will be useful also in the study
of spin glasses.
Receveid 19 May 1998 相似文献
4.
A. Benyoussef D. Dohmi A. El Kenz L. Peliti 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(4):503-510
Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition
in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals
to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that,
the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been
predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We
have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled
phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases
becomes first order.
Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998 相似文献
5.
We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose
a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function
instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid
interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained
for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat
asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical
species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption,
leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed
(or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases,
the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface.
The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider
the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain
at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface.
Received 21 January 1999 相似文献
6.
We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to
fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001) to rigorously compute the free energy. In the case of pairwise interactions (p=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization
for all values of external parameters. Our analysis also works for even p≥4 except in a range of parameters surrounding the phase transition line, and for odd p≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play
a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems
related to communication over a noisy channel, and is briefly explained. 相似文献
7.
The construction of physical models with local time‐reparametrization invariance is reviewed. Negative‐energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant Hamilton‐Jacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the Friedmann‐Lemaître‐Robertson‐Walker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a σ‐model on some scalar manifold. An explicit gauge‐invariant solution is constructed for the non‐linear O(N)‐models. 相似文献
8.
A. Montanari F. Ricci-Tersenghi 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(3):339-346
The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking
(1RSB) ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry breaking (FRSB) phase, is often regarded as an inessential, and
somehow exotic phenomenon. In this paper we show that the metastable states which are relevant for the out-of-equilibrium
dynamics of such systems are always in a FRSB phase. The only exceptions are (to the best of our knowledge) the p-spin spherical model and the random energy model (REM). We also discuss the consequences of our results for aging dynamics
and for local search algorithms in hard combinatorial problems.
Received 10 February 2003 Published online 20 June 2003
RID="a"
ID="a"e-mail: Federico.Ricci@roma1.infn.it
RID="b"
ID="b"UMR 8549, Unité Mixte de Recherche du Centre National de la Recherche Scientifique et de l' école Normale Supérieure 相似文献
9.
H. Feldmann R. Oppermann 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(3):429-445
We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin
glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for
all temperatures T and chemical potentials μ. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic
interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity
are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum
Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are
presented together with a few results for -step breaking. Suppression of reentrant SG-SC-SG transitions due to RPSB is found and discussed in context of ferromagnet-SG
boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments
in heavy fermion systems and high superconductors. We find a crossover line traversing the SG-phase with as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates
a random field instability and suggest Dotsenko-Mézard vector replica symmetry breaking to occur at low temperatures beyond.
Received 26 November 1998 and Received in final form 25
January 1999 相似文献
10.
Francesco Guerra 《Communications in Mathematical Physics》2003,233(1):1-12
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean
field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument
in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy
is bounded from below by the value given in the Parisi Ansatz, uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum
rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick
approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.
Received: 6 May 2002 / Accepted: 6 September 2002 Published online: 13 January 2003 相似文献
11.
S. Boettcher 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(1):29-39
The average ground state energy and entropy for ±J spin glasses on Bethe lattices of connectivities k + 1 = 3..., 26 at T = 0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n = 212), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies
per spin ek+1 but also for their entropies sk+1. The results indicate sizable differences between lattices of even and odd connectivities. The extrapolated ground state
energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all
even connectivities k + 1 to within a fraction of a percent onto a simple functional form, e
k + 1 = E
SK
- (2E
SK + )/, where E
SK = - 0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form
is in conflict with perturbative calculations at large k + 1, which do not distinguish between even and odd connectivities. We also find non-zero entropies per spin sk+1 at small connectivities. While sk+1 seems to vanish asymptotically with 1/(k + 1) for even connectivities, it is numerically indistinguishable from zero already for odd k + 1 ≥ 9.
Received 9 August 2002 Published online 27 January 2003
RID="a"
ID="a"e-mail: sboettc@emory.edu www.physics.emory.edu/faculty/boettcher 相似文献
12.
S.C. Manrubia U. Bastolla A.S. Mikhailov 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(4):497-508
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of
synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting attractors and
might be viewed as dynamical glasses. Glass properties of GCLM in the thermodynamical limit of large system sizes N are investigated. Replicas, representing orbits that start from various initial conditions, are introduced and distributions
of their overlaps are numerically determined. We show that for fixed-field ensembles of initial conditions all attractors
of the system become identical in the thermodynamical limit up to variations of order 1/, and thus replica symmetry is recovered for N→∞. In contrast to this, when fluctuating-field ensembles of initial conditions are chosen, replica symmetry remains broken
in the thermodynamical limit.
Received 9 July 2001 相似文献
13.
H. Niggemann J. Zittartz 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(4):731-738
We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5
continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and
rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local
fluctuations and longitudinal and transversal two-point correlation functions.
Received 1 March 1999 相似文献
14.
E. Brézin C. De Dominicis 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,24(3):353-358
One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states
at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two parallel
limiting planes, generate an interface and a cost in free energy per unit area of the interface. For continuum symmetries
the order parameter interpolates smoothly between the end planes carrying two different directions of the order parameter.
The cost in free energy is then proportional to Ld-2 for a system of characteristic size L. The power of L is related to the lower critical dimension, and the coefficient of this additional free energy vanishes at the critical temperature.
In this note it is shown within a loop expansion that one does find the expected behavior of this twist free energy. This
is a preamble to the study of situations where the broken continuum symmetry is believed to be more complex, as in Parisi
ansatz for the Edwards-Anderson spin glass.
Received 11 June 2001 相似文献
15.
T. Temesvári C. De Dominicis I.R. Pimentel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(3):361-372
Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant
to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two
different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica
magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line,
along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper
critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical
role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is
introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex
rules are presented to help future renormalisation-group calculations.
Received 9 October 2001 相似文献
16.
We review the thermodynamical properties of the (super)membranes in canonical ensemble. The free energy for flat supermembranes and for compactified supermembranes is calculated in semiclassical approximation. The corresponding extension for super-p-branes is also presented. The presence of the Hagedorn temperature which depends on the cut-off parameter is found. It is shown that the free energy for (super)membranes can be presented in modular invariant form (SL(2, Z) invariance). Some connected problems (the calculation of the static potential, the probable dual symmetry) for bosonic p-brane are also discussed. 相似文献
17.
Bang-qing Xu Peng Xu Dianyan Xu Chang-gui Shao 《International Journal of Theoretical Physics》1994,33(12):2389-2398
By means of the identity operator and vertex operator technique, reparametrization invariance and BRST symmetry are proven for the heterotic string with Wess-Zumino term coupling the fiber bundle. The motion space of the string is assumed to be a direct productM
d
G of a Minkowski spaceM
d
of dimensiond with an intrinsic group manifoldG of dimensiond
G
, and turns out to give the critical dimension. 相似文献
18.
Fu Hai Su Kun Ding Yuangfang Liu Wei Chen 《Journal of Physics and Chemistry of Solids》2006,67(11):2376-2381
The temperature and pressure dependences of band-edge photoluminescence from ZnO microrods have been investigated. The energy separation between the free exciton (FX) and its first order phonon replica (FX-1LO) decreases at a rate of kBT with increasing temperature. The intensity ratio of the FX-1LO to the bound exciton (BX) emission is found to decrease slightly with increasing pressure. All of the exciton emission peaks show a blue shift with increasing pressure. The pressure coefficient of the FX transition, longitudinal optical (LO) phonon energy, and binding energy of BX are estimated to be 21.4, 0.5, and 0.9 meV/GPa, respectively. 相似文献
19.
T. Temesvári C. De Dominicis I. Kondor 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(4):629-634
Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We
argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling
forms cannot be expanded in term of the coupling constant w2. Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual
behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter
w2 and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared
divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed.
Received 23 December 1998 and Received in final form 23 March 1999 相似文献
20.
M. Picco F. Ritort M. Sales 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(4):565-582
The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece
[2,3] which show that two of these parameters, G and G
c, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal
symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model
with and without a field and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite
volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore,
a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information
can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than
the Binder cumulant for T
c and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters
defined in terms of connected quantities are the proper ones to look at.
Received 20 September 2000 and Received in final form 10 January 2001 相似文献