Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

1952 ◽  
Vol 87 (3) ◽  
pp. 410-419 ◽  
Author(s):  
T. D. Lee ◽  
C. N. Yang
Keyword(s):  
Statistical Theory ◽  
Phase Transitions ◽  
Ising Model ◽  
Lattice Gas ◽  
Equations Of State

scholarly journals Concepts on statistical physics - fluctuations in equilibrium

2015 ◽  
Vol 4 (1) ◽  
pp. 1-27
Author(s):  
L´eon Brenig
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Exponents ◽  
Statistical Models ◽  
Statistical Physics ◽  
Lattice Gas ◽  
Simple Fluids ◽  
Large Numbers ◽  
Starting Point

This essay corresponds to the content of three lectures about statistical physics delivered to the audience of the 2014 section of the R. A. Salmeron School of Physics, at the UnB. Our starting point was very simple statistical models (lattice gas, spin-1/2 ferromagnet), used as illustrations of the competencies and methods in statistical physics. Thus we introduce the Gibbs ensembles, defining a connection with thermodynamics and discussing the role played by fluctuations and large numbers. We present phenomenological aspects of phase transitions and critical phenomena in simple fluids and in uniaxial ferromagnets, emphasizing the universal character of the critical exponents. We describe the phenomenological van der Waals and Curie-Weiss theories and the Landau expansion, which are present-day relevant methods, despite the fact that such theories give rise to critical exponents in disagreement with experiments. We present then the paradigmatic Ising model, which points us to a way to overcome the phenomenological results. A brief presentation of the scale phenomenological methods and the contemporaneous renormalization group are considered at the end of these lectures.

Monte Carlo study of phase transitions in an Ising model superlattice

1991 ◽  
Vol 69 (8) ◽  
pp. 6158-6160 ◽  
Author(s):  
Jialin Li ◽  
D. P. Landau
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Ising Model ◽  
Monte Carlo Study
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