scholarly journals Nonequilibrium second-order phase transitions in stochastic lattice systems: A finite-size scaling analysis in two dimensions

1988 ◽  
Vol 51 (1-2) ◽  
pp. 321-321
Author(s):  
J. L. Vall�s ◽  
J. Marro
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Two Dimensions ◽  
Second Order ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Lattice Systems ◽  
Size Scaling

Finite-size scaling analysis of isotropic–polar phase transitions in an amphiphilic fluid

2011 ◽  
Vol 24 (3) ◽  
pp. 035103 ◽  
Author(s):  
Michael Melle ◽  
Stefano Giura ◽  
Sergej Schlotthauer ◽  
Martin Schoen
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Scaling Analysis ◽  
Polar Phase ◽  
Finite Size Scaling ◽  
Size Scaling

CLASSIFICATION THEORY FOR PHASE TRANSITIONS

1993 ◽  
Vol 07 (26) ◽  
pp. 4371-4387 ◽  
Author(s):  
R. HILFER
Keyword(s):  
Phase Transitions ◽  
Classification Scheme ◽  
Equilibrium Phase ◽  
Finite Size ◽  
Second Order ◽  
Classification Theory ◽  
Special Role ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling

A refined classification theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two independent generalizations of Ehrenfests traditional classification scheme. The statistical mechanical classification theory is based on generalized limit theorems for sums of random variables from probability theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without renormalization group methods. The classification distinguishes two fundamentally different types of phase transitions. Phase transitions of order λ>1 correspond to well known equilibrium phase transitions, while phase transitions with order λ<1 represent a new class of transitions termed anequilibrium transitions. The generalized order λ varies inversely with the strength of fluctuations. First order and second order transitions play a special role in both classification schemes. First order transitions represent a limiting case separating equilibrium and anequilibrium transitions. The special role or second order transitions is shown to be related to the breakdown of hyperscaling. For anequilibrium transitions the nature of the heat bath in the canonical ensemble becomes important.

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