scholarly journals Renewal properties of the d = 1 Ising model

2018 ◽  
Vol 30 (09) ◽  
pp. 1850018
Author(s):  
Marzio Cassandro ◽  
Immacolata Merola ◽  
Errico Presutti
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Renewal Process ◽  
Infinite Sequence ◽  
Mean Field ◽  
Coarse Graining ◽  
Inverse Temperature ◽  
Scaling Parameter ◽  
Kac Potentials ◽  
The Mean

We consider the [Formula: see text] Ising model with Kac potentials at inverse temperature [Formula: see text] where the mean field predicts a phase transition with two possible equilibrium magnetizations [Formula: see text], [Formula: see text]. We show that when the Kac scaling parameter [Formula: see text] is sufficiently small, typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is “close” to [Formula: see text], and respectively, [Formula: see text]. We prove that the corresponding marginal of the unique DLR measure is a renewal process.

scholarly journals Phase diagram of the selfinteracting particle­-antiparticle boson system

2021 ◽  
Vol 29 (1) ◽  
pp. 5-14
Author(s):  
D. Anchishkin ◽  
V. Gnatovskyy ◽  
D. Zhuravel ◽  
V. Karpenko
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Diagrams ◽  
Canonical Ensemble ◽  
Bose Condensate ◽  
Mean Field ◽  
Thermodynamic Quantities ◽  
Boson System ◽  
The Mean

A system of interacting relativistic bosons at finite temperatures and isospin densities is studied within the framework of the Skyrme­like mean­field model. The mean field contains both attractive and repulsive terms. The consideration is taken within the framework of the Canonical Ensemble and the isospin­density dependencies of thermodynamic quantities is obtained, in particular as the phase diagrams. It is shown that in such a system, in addition to the formation of a Bose­Einstein condensate, a liquid­gas phase transition is possible. We prove that the multi­boson system develops the Bose condensate for particles of high­density component only.

FAILURE OF A MEAN-FIELD APPROACH FOR THE MILLER–HUSE PHASE TRANSITION

2000 ◽  
Vol 10 (01) ◽  
pp. 251-256 ◽  
Author(s):  
FRANCISCO SASTRE ◽  
GABRIEL PÉREZ
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Chaotic Maps ◽  
Initial Conditions ◽  
Mean Field ◽  
Region Of Interest ◽  
Universality Class ◽  
Two Dimensional ◽  
Field Approach

The diffusively coupled lattice of odd-symmetric chaotic maps introduced by Miller and Huse undergoes a continuous ordering phase transition, belonging to a universality class close but not identical to that of the two-dimensional Ising model. Here we consider a natural mean-field approach for this model, and find that it does not have a well-defined phase transition. We show how this is due to the coexistence of two attractors in its mean-field description, for the region of interest in the coupling. The behavior of the model in this limit then becomes dependent on initial conditions, as can be seen in direct simulations.

Single-Crystal Magnetic Properties of [Co(NH3)5(OH2)] [Cr(CN)6] Between 2 and 300 K

1992 ◽  
Vol 45 (11) ◽  
pp. 1899 ◽  
Author(s):  
PA Reynolds ◽  
CD Delfs ◽  
BN Figgis ◽  
B Moubaraki ◽  
KS Murray
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Mean Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Zero Field Splitting ◽  
Magnetic Exchange Interaction ◽  
Mean Field Model ◽  
Magnetic Exchange ◽  
The Mean

The magnetic susceptibilities along and perpendicular to the c axis (hexagonal setting) between 2.0 and 300 K at a magnetic field of 1.00 T, and the magnetizations at field strengths up to 5.00 T, are presented for single crystals of [Co(NH3)5(OH2)] [Cr(CN)6]. The results are interpreted in terms of zero-field splitting (2D) of the ground 4A2g term by spin-orbit coupling and of magnetic exchange interaction between the chromium atoms. The magnetic exchange is modelled as one of Ising or mean-field in type. The exchange is found to be quite small: J = -0.18(6) cm-1 if the Ising model is employed, and -0.03(1) cm-1 for the mean-field model. The model adopted for the exchange has a strong influence on the value of the parameter D obtained. When the Ising model is used D is deduced to be -0.28(9) cm-l; when the mean-field model is used D is -0.14(4) cm-l. The g-values deduced are in agreement with those from e.s.r. measurements at higher temperatures and do not depend on the exchange model. In any case, D is found to be sufficiently large that it must be considered in a polarized neutron diffraction experiment on the compound.

On the mean-field Ising model in a random external field

1985 ◽  
Vol 41 (1-2) ◽  
pp. 299-313 ◽  
Author(s):  
S. R. Salinas ◽  
W. F. Wreszinski
Keyword(s):  
Ising Model ◽  
External Field ◽  
Mean Field ◽  
The Mean ◽  
Random External Field

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

Analytical solution of the mean field Ising model for finite systems

2012 ◽  
Vol 24 (22) ◽  
pp. 226004 ◽  
Author(s):  
Dalía S Bertoldi ◽  
Eduardo M Bringa ◽  
E N Miranda
Keyword(s):  
Ising Model ◽  
Analytical Solution ◽  
Mean Field ◽  
Finite Systems ◽  
The Mean

scholarly journals Generalization of the mean-field Ising model within Tsallis thermostatistics

1997 ◽  
Vol 238 (1-4) ◽  
pp. 285-294 ◽  
Author(s):  
Fevzi Büyükkiliç ◽  
Doǧan Demirhan ◽  
Uǧur Tirnakli
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
The Mean

Phase Transitions and the Ising Model

2019 ◽  
pp. 423-446
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Landau Theory ◽  
Magnetic Moments ◽  
Mean Field ◽  
Higher Dimensions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ising Chain ◽  
The Mean

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.

Sign in / Sign up

Export Citation Format

Share Document