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1.
Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition. 相似文献
2.
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with random magnetic interaction. The thermodynamics is worked out in the full replica symmetry breaking scheme. The model exhibits a high temperature/low density paramagnetic phase. As temperature decreases or density increases, a phase transition to a full replica symmetry breaking spin-glass phase occurs. The nature of the transition can be either of the second order or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter, a latent heat, and coexistence of phases. 相似文献
3.
4.
We analyze the Blume-Emery-Griffiths-Capel model with disordered interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram, and the transition lines are computed using the full replica symmetry breaking ansatz. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase. 相似文献
5.
The Bethe lattice spin glass revisited 总被引:2,自引:0,他引:2
M. Mézard G. Parisi 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(2):217-233
So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong
in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution
have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature.
Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level
of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical
simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.
Received 27 September 2000 相似文献
6.
Terufumi Yokota 《Physica A》2008,387(14):3495-3502
Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops. 相似文献
7.
A constructive scheme for determining pure states at very low temperature in the 3-spins glass model on a random lattice is provided, in full agreement with Parisi's one step replica symmetry breaking (RSB) scheme. Proof is based on the analysis of a partial decimation procedure and of the statistical properties of its output, i.e., a reduced Hamiltonian acting on a subset of the initial spins. The number of ground states (GS) in each state, the number of states, and the distances between GS are calculated and correspond to RSB predictions. 相似文献
8.
The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step replica symmetry breaking. The transition from the replica symmetric solution to the replica replica symmetry broken one is either continuous or discontinuous inq
1–q0 depending on the strength of the external magnetic field. The model can be solved explicitly for anyp at any temperature and magnetic field. Below the transition we find an infinite number of metastable states. 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.
T. Castellani F. Krzakala F. Ricci-Tersenghi 《The European Physical Journal B - Condensed Matter and Complex Systems》2005,47(1):99-108
We derive the zero-temperature phase diagram of spin glass models with
a generic fraction of ferromagnetic interactions on the Bethe lattice.
We use the cavity method at the level of one-step replica symmetry
breaking (1RSB) and we find three phases: a replica-symmetric (RS)
ferromagnetic one, a magnetized spin glass one (the so-called mixed
phase), and an unmagnetized spin glass one. We are able to give
analytic expressions for the critical point where the RS phase becomes
unstable with respect to 1RSB solutions: we also clarify the mechanism
inducing such a phase transition. Finally we compare our analytical
results with the outcomes of a numerical algorithm especially designed
for finding ground states in an efficient way, stressing weak points
in the use of such numerical tools for discovering RSB effects. Some
of the analytical results are given for generic connectivity. 相似文献
11.
Journal of Statistical Physics - In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that... 相似文献
12.
《Physica A》1996,229(2):181-187
The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method. 相似文献
13.
In the spin glass phase near the critical temperature we find in aparticular replica symmetry breaking pattern an order parameter with free energy greater than that of the Parisi's. 相似文献
14.
The quantum spherical spin-glass is analyzed by using a replica symmetric theory (RS) and the physical properties of the system can be explained by the existence of a zero frequency condensate below the critical temperature. The free energy coincides with previous results obtained with an annealed average of the partition function. A calculation with one step replica symmetry breaking (1S-RSB) shows that the only solution is the replica symmetric one. 相似文献
15.
G.R. Schreiber 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,9(3):479-490
A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution
with ferromagnetic mean . Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions
of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been
argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with
respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically.
Received 13 January 1997 相似文献
16.
For five different Heisenberg spin glass systems, torque experiments were performed in applied magnetic fields up to 4 T. The Dzyaloshinski-Moriya random anisotropy strengths, the in-field torque onset temperatures, and the torque relaxation were measured. Critical exponents were estimated independently using a standard protocol. The data are strong evidence for a true spin glass ordered state which survives under high applied magnetic fields; they can be interpreted consistently in terms of a chiral ordering model with replica symmetry breaking as proposed by Kawamura and co-workers. 相似文献
17.
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
18.
Olivier Rivoire 《Journal of statistical physics》2004,117(3-4):453-476
The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare samples in spin glass like models. This relation between large deviations and replica theory is explicited on different models where it is confronted to direct combinatorial calculations. 相似文献
19.
We study a system of Ising spins with quenched random infinite ranged p-spin interactions. For p → ∞, we can solve this model exactly either by a direct microcanonical argument, or through the introduction of replicas and Parisi's ultrametric ansatz for replica symmetry breaking, or by means of TAP mean field equations. Although the model is extremely simple it retains the characteristic features of a spin glass. We use it to confirm the methods that have been applied in more complicated situations and to explicitlu exhibit the structure of the spin glass phase. 相似文献
20.
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows describing the transition from the full replica symmetry breaking glass solution to stable first replica symmetry breaking glass solution in the case of non-reflective symmetry diagonal operators used instead of Ising spins. As an example, axial quadrupole moments in place of Ising spins are considered and the boundary value \({p_{{c_1}}} \cong 2.5\) is found. 相似文献