首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.  相似文献   

2.
We consider a dilute classical gas in a volume –1 which tends to d by dilation as 0. We prove that the pressurep(–1) isC q in at =0 (thermodynamic limit), for anyq, provided the boundary isC q and provided the Ursell functionsu n (x 1, ...,x n) admit moments of degreeq and have nice derivatives.  相似文献   

3.
Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form S= L 1 d 4 x+ L 2 d 4 x where the volume element d 4 x is independent of the metric. For global scale invariance, a dilaton has to be introduced, with non-trivial potentials V()=f 1 e in L 1 and U()=f 2 e 2 in L 2 . This leads to non-trivial mass generation and a potential for which is interesting for inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for Quintessential models, which are scale invariant but formulated with the use of volume element d 4 x alone. For closed strings and branes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants.  相似文献   

4.
The validity of the finite-size scaling prediction about the existence of logarithmic corrections in the helicity modulus of three-dimensional O(n)-symmetric order parameter systems in confined geometries is studied for the three-dimensional mean spherical model of geometryL 3/s-d×d, 0d<3. For a fully finite geometry the general case ofd p0 periodic,d a0 antiperiodic,d 00 free, andd 10 fixed (d p+da+d0+d1=d, d=3) boundary conditions is considered, whereas for film (d=2) and cylinder (d=1) geometries only the case of antiperiodic and/or periodic boundary conditions is investigated. The corresponding expressions for the finite-size scaling function of the helicity modulus and its asymptotics in the vicinity, below, and above the bulk critical temperatureT c and the shifted critical temperatureT c,L are derived. The obtained results are not in agreement with the hypothesis of the existence of a log(L) correction term to the finite-size behavior of the helicity modulus in the finite-size critical region if d=3. In the case of film and cylinder geometries there are no logarithmic corrections. In the case of a fully finite geometry a universal logarithmic correction term –[(d 0d 1)/4–2da–1/2] lnL/L is obtained only for (T c-T) LlnL.  相似文献   

5.
The mathematical relationship between the orientational order parameters and the coherent neutron scattering cross section for a nematic liquid crystal is given. For deuterated para-azoxyanisole the single-molecule part of the cross section is evaluated within the meanfield approximation and combined with experimental results to give information about molecular orientational order in terms of P 2, P 4 and P 6. Both P 2 and P 4 are found necessary for describing the molecular order. Discrepancies between experimental and theoretical results are interpreted as possibly reflecting the inadequacy of the meanfield theory of Maier and Saupe.  相似文献   

6.
A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L dd × d ( d 2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For j 0, jd-d, no seams are present except at infinity, whereas if j = 1/2, impurity saturation occurs. For 0 < j < 1/2 the physical domain phys =D dd × d (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T 0). Below that temperature (T>T 0), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition.  相似文献   

7.
Using the formalism developed in earlier work, dimensional crossover on ad-dimensional layered Ising-type system satisfying periodic boundary conditions and of sizeL is considered belowT c (L), T c (L) being the critical temperature of the finite-size system. Effective critical exponents eff and eff are shown explicitly to crossover between theird- and (d–1)-dimensional values for L in the limitsL/ L andL/ L 0, respectively, L , being the correlation length in the layers. Using anL-dependent renormalization group, the effective exponents are shown to satisfy natural generalizations of the standard scaling laws. In addition,L-dependent global scaling fields which span the entire crossover are defined and a scaling form of the equation of state in terms of them derived. All the above assertions are verified explicitly to one loop in perturbation theory, in particular effective exponents and a universal crossover equation of state are obtained and shown in the above asymptotic limits to be in good agreement with known results.  相似文献   

8.
Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by m (L)=(Inq/E)L –d +O(L –2d ) with respect to the infinite-volume transition point t . We also propose an alternative definition of the finite-volume transition temperature t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from t .  相似文献   

9.
Systems representable as a time-dependent Ginzburg-Landau model with nonconserved order parameter are considered in a block (V=L d) geometry with periodic boundary conditions, both for space dimensionalitiesd4 andd=4–. A systematic approach for studying finite size effects on dynamic critical behavior is developed. The method consists in constructing an effective reduced dynamics for the lowest-energy (q=0) mode by integrating out the remaining degrees of freedom, and generalizes recent analytic approaches for studying static finite size effects to dynamics. Above four dimensions, the coupling to the other (q0) modes is irrelevant and the probability densityP(,t) for the normalized order parameter=dd x(x,t)/V satisfies a Fokker-Planck equation. The dynamics is equivalently described by the Langevin equation for a particle moving in a ||4 potential or by a supersymmetric quantum mechanical Hamiltonian. Dynamic finite size scaling is found to be broken, e.g. the order parameter relaxation rate varies at the bulk critical temperatureT c, as (T c, L)L –d/2 asL. By contrast, ford<4, the coupling to the other (q0) modes cannot be ignored and dynamic finite size scaling is valid. The asymptotic behavior of correlation and response functions can be studied within the framework of an expansion in powers of 1/2. The scaling function associated with is computed to one-loop order. Finally, the many component (n) limit is briefly considered.  相似文献   

10.
We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae 2 p (1+a 1 e + ...) as , with p1. The staggered susceptibility behaves as stagg 5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.  相似文献   

11.
We consider simple cubic lattice systems ind dimensions with a continuous real charge variableq(n) at each lattice siten. These variables are subject t'o a mean spherical constraint forcing n q 2(n)=Q 2, where is the number of lattice sites in andQ is an elementary charge. The energy of the charges comes from interactions with an electrostatic potential, which is the solution of a symmetric second-difference Poisson equation on the lattice. Two cases are considered, both of which allow the inclusion of the effects of a fixed, constant, external electric field. On the lattice 1=[1,N]d , a Neumann condition is imposed at the surface of the lattice. The lattice 2=[1,N] [–M,M](d–1) is periodic in each direction ranging over [–M, M] and has a Dirichlet condition imposed at the other two surfaces. On 2 a finite electric field may be applied, while on 2 a finite potential difference may be applied across the lattice. The models are exactly solvable. We study the distribution functions on each system and show that they satisfy appropriate forms of the first two Stillinger-Lovett moment conditions. The two charge distribution functions show screening behavior at high temperature and extreme short range at an intermediate temperatureT 0(d), and oscillate as they decay to zero forT<T 0(d). Because of the continuous nature of the charge variables, there is no Kosterlitz-Thouless transition in two dimensions. In three dimensions the change in the decay behavior of the distribution functions atT<T 0(d) is precursor to a phase transition to a charge ordered state.  相似文献   

12.
The resistivity (100 K) scatters very much for YBa2Cu3Ox prepared as single crystals, epitaxial films or bulk samples which consist of grains of 1 to 10 m diameter. An analysis of (T) for granular bulk samples is presented indicating the existence of a low intrinsic resistivity i (T)= 0L i + i T with 0L i 0 and i 0.5µcm/K. The large grain boundary resistivity b between the grains (>1 m) yield a macroscopic percolative conduction path lengtheningL/L 0>1 with a reduced effective cross sectionC<C 0 and thus, (T)= b +(LC 0/L 0 C i (T). Evidence is presented for weak links inside single crystals and grains.  相似文献   

13.
Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h 2 are found to behave—lnFlnh 2(T R T)–1 for temperaturesT approachingT R from below. The linear relaxation rate of the order parameter is found to be proportional to –2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT R , shows a metastable regime belowT R with a spinodal limit of metastability c , beyond which oscillatory growth starts. The critical behavior of c is found to be ln c –(T R T)–1+O(ln (T R T)).  相似文献   

14.
The dually conjugate Hopf superalgebras Fun p,q (GL(11)) and U p,q (gl(11)) are studied using the Frønsdal-Galindo approach and the full Hopf structure of U p,q (gl(11)) is extracted. A finite expression for the universal T-matrix, identified with the dual form and expressing the generalization of the exponential map of the classical groups, is obtained for Fun p,q (GL(11)). In a representation with a colour index, the T-matrix assumes a form that satisfies a coloured graded Yang-Baxter equation.  相似文献   

15.
The self-avoiding walk in a quenched random environment is studied using real-space and field-theoretic renormalization and Flory arguments. These methods indicate that the system is described, ford c =4, and, for large disorder ford>d c , by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk,LN p withN the number of steps, and the fluctuations in the free energy,fL p. The bound 1/-d/2 is obtained. Exact results on hierarchical lattices yield> pure and suggests that this inequality holds ford=2 and 3, although= pure cannot be excluded, particularly ford=2. Ford>d c there is a transition between strong and weak disorder phases at which= pure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized.  相似文献   

16.
We calculate the moments t q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t q ~L (q) asL, then we show that there is a phase transition atq=q c such that whenq<q c ,(g)=0, and forq>q c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.  相似文献   

17.
We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields cL –2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ c ) –v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from c be no larger thanL –2. Otherwise, crossover behavior will be observed.  相似文献   

18.
Our investigation of the electrical resistivity (T) betweenT=0.1 K and 295 K revealed for all Fe-concentrations, 2.4x16, a minimum of betweenT min=7 K and 15 K. Above the minimum, scattering from structural disorder prevails in the paramagnetic alloy (x=2.4), while in the ferromagnetic glasses (x5.6) coherent magnon scattering appears to dominate. With one exception, (TT min) increases as down to the lowest temperatures for all investigated Fe-contents (x10.4) in zero magnetic field as well as in applied 6 T. The value of the slopes, 6.3(6) ( cm)–1 K–1/2, agrees with the universal scaling behaviour reported recently by Cochrane and Strom-Olsen for systems with strong electron-electron interaction. A large, linear rise of (T<T min,B=0) observed in the most diluted sample (x=2.4) is tentatively attributed to quantum localization in the non-reentrant spin glass phase. The magnitude of the temperature effects on (T) above as well as belowT min indicates significantd-band contributions to the conductivity.  相似文献   

19.
The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space . The rigorous upper bound (mf) = ( – 1)/ for the order parameter 2, is given by the correlation identity and the FKG inequality. Then an improvement of this bound (mf) is shown in a similar fashion; C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense.  相似文献   

20.
In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter i j k are the same as those of the magnetization i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ e independent of the way in which the odd interactionsJ o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号