Finite-size scaling at first- and second-order phase transitions of Baxter–Wu model

2005 ◽  
Vol 355 (2-4) ◽  
pp. 393-407 ◽  
Author(s):  
S.S. Martinos ◽  
A. Malakis ◽  
I. Hadjiagapiou
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Second Order ◽  
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.

scholarly journals Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

2009 ◽  
Vol 80 (5) ◽  
Author(s):  
L. A. Fernandez ◽  
A. Gordillo-Guerrero ◽  
V. Martin-Mayor ◽  
J. J. Ruiz-Lorenzo
Keyword(s):  
Phase Transitions ◽  
Specific Heat ◽  
Finite Size ◽  
Second Order ◽  
Finite Size Scaling ◽  
Size Scaling

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

scholarly journals PERCOLATION AND FINITE SIZE SCALING IN SEVEN DIMENSIONS

2004 ◽  
Vol 15 (09) ◽  
pp. 1321-1325
Author(s):  
LOTFI ZEKRI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Numerical Investigation ◽  
Critical Exponents ◽  
Finite Size ◽  
Critical Dimension ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Hypercubic Lattice

Numerical investigation of critical exponents on a hypercubic lattice with Ld random sites with L up to 33 and d up to 7 showed that above the critical dimension the phase transitions in Ising model and percolation are not alike.

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