Finite-size effects at the first-order phase transition in the three-dimensional Heisenberg model

1992 ◽  
Vol 46 (2) ◽  
pp. 937-943 ◽  
Author(s):  
Kun Chen ◽  
D. P. Landau
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Size Effects ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Finite Size ◽  
Finite Size Effects ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

Finite-size effects of linear sigma model in compactified space–time

2014 ◽  
Vol 29 (15) ◽  
pp. 1450078 ◽  
Author(s):  
Tran Huu Phat ◽  
Nguyen Van Thu
Keyword(s):  
Phase Transition ◽  
Sigma Model ◽  
Finite Size ◽  
Casimir Energy ◽  
Linear Sigma Model ◽  
Finite Size Effects ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Compactified Space

The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV . When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.

FINITE-SIZE SCALING ANALYSIS OF THE DECAY OF AN UNSTABLE STATE DURING A FIRST ORDER PHASE TRANSITION

1988 ◽  
Vol 02 (02) ◽  
pp. 527-536 ◽  
Author(s):  
JORGE VIÑALS ◽  
DAVID JASNOW
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Structure Factor ◽  
Order Parameter ◽  
Finite Size ◽  
Unstable State ◽  
Finite Size Scaling ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

We extend standard finite-size scaling methods to study the dynamical evolution of an unstable state far from equilibrium as the system undergoes a first order phase transition. We suggest that the nonequilibrium structure factor S(q, t, L), at late times and for large enough lattice sizes, scales as S(q, t, L)=LdF(qL, t1/x/L). L is the linear dimension of the system and 1/x is the domain growth exponent. We obtain x=2 in the case of the kinetic Ising model with a nonconserved order parameter. For a critical quench in a system with conserved order parameter, scaling of the peak of the structure factor gives 1/x≈0.27. Higher wavenumbers, however, are more consistent with x=3.

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