Nonsymmetric first-order transitions: Finite-size scaling and tests for infinite-range models

1990 ◽  
Vol 60 (5-6) ◽  
pp. 551-560 ◽  
Author(s):  
V. Privman ◽  
J. Rudnick
Keyword(s):  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
Infinite Range

scholarly journals Transmuted Finite-size Scaling at First-order Phase Transitions

2014 ◽  
Vol 57 ◽  
pp. 68-72 ◽  
Author(s):  
Marco Mueller ◽  
Wolfhard Janke ◽  
Desmond A. Johnston
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
First Order Phase

A MICROSCOPIC THEORY OF FINITE-SIZE SCALING

1992 ◽  
Vol 03 (05) ◽  
pp. 897-912 ◽  
Author(s):  
CHRISTIAN BORGS
Keyword(s):  
Finite Size ◽  
Microscopic Theory ◽  
Finite Size Scaling ◽  
Rigorous Theory ◽  
First Order ◽  
Mathematical Proofs ◽  
Mass Gap ◽  
Size Scaling ◽  
Main Emphasis ◽  
Cubic Systems

In this paper, I give an overview over a recently developed rigorous theory of finite-size scaling near first order transitions. Leaving out details of the mathematical proofs, the main emphasis is put on the underlying physical ideas and the discussion of the validity of the results for regions which are, in the sense of mathematical rigour, not covered by the original papers. I present both the finite-size scaling for cubic systems and for long cylinders, discussing also a recent controversy which stems from our work on the finite-size scaling of the mass gap in long cylinders.

scholarly journals Finite-size scaling at the first-order quantum transitions of quantum Potts chains

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Massimo Campostrini ◽  
Jacopo Nespolo ◽  
Andrea Pelissetto ◽  
Ettore Vicari
Keyword(s):  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
Quantum Transitions

scholarly journals Finite-size scaling for first-order transitions: Potts model

1995 ◽  
Vol 80 (5-6) ◽  
pp. 1433-1442 ◽  
Author(s):  
P. M. C. de Oliveira ◽  
S. M. Moss de Oliveira ◽  
C. E. Cordeiro ◽  
D. Stauffer
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
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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