Search results for "Phase Transition"

Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model

1995

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.…

SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS

1992

The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transiti…

Effects of heat flux on lambda transition in liquid 4He,

2014

This paper is concerned with the derivation of a phase field model for λ-transition in 4He, when the liquid is subject to pressure and heat flux. As parameter that controls the transition, a field f that is the geometrical mean between the density of the fluid and that of the superfluid is used. The resulting model, that is a generalization of previous papers on the same subject, chooses as field variables the density, the velocity, the temperature and the heat flux, in addition to this field f. The restrictions on the constitutive quantities are obtained by using the Liu method of Lagrange multipliers. New results with respect to previous models are the presence of non-local terms to descr…

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

1993

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

1994

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.

Noise-Induced Phase Transitions

2009

Finite-size scaling for a first-order transition where a continuous symmetry is broken: The spin-flop transition in the three-dimensional XXZ Heisenb…

2019

Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological ``degeneracy'' factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, $XXZ$ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ simple cubic lattice for the first-order ``spin-flop'' transition between the Ising-like antiferromagnetic state and the canted, $XY$-like state. Our theory predicts that for large linear dimension $L$ the field dependen…

Cluster Algorithms and Reweighting Methods

2019

Roughly at the time (1987) when the manuscript for the first three chapters of the present book was completed, several breakthroughs occurred. They had a profound influence on the scope of Monte Carlo simulations in statistical physics, particularly for the study of phase transitions in lattice models.

Scaling Behavior of the 2D XY Model Revisited

1998

Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square L × L lattices, the scaling behavior of the susceptibility χ and correlation length ξ in the vicinity of the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (ln ξ)-2r in the high-temperature phase and (ln L)-2r in the finite-size scaling region, respectively.

Corner contribution to cluster numbers in the Potts model

2013

For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of Gamma. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are no…