Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-ph/9403310 · Physical Review Letters

Dynamics of Weak First Order Phase Transitions

Marcelo Gleiser

Published Dec 26, 1994• 45 citations
arXivHTMLPDF

Abstract

The dynamics of weak vs strong first order phase transitions is investigated numerically for (2 + 1)-dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition, with the order parameter being the equilibrium fractional population difference between the two phases at the critical temperature, and the control parameter being the coefficient of the cubic coupling in the free-energy density. The critical point is identified, and a power law controlling the relaxation dynamics at this point is obtained. Possible applications are briefly discussed.

DOI
10.1103/physrevlett.73.3495

Related papers

Dynamic approach to weak first-order phase transitions

Lothar Schülke, Bo Zheng

A short-time dynamic approach to weak first-order phase transitions is proposed. Taking the two-dimensional Potts models as examples, from short-time behavior of nonequilibrium relaxational processes starting from high temperature and zero temperature states, pseudo-critical-points K* and K** are determined. A clear difference of the values for K* and K** distinguishes a weak first-order transition from a second-order one.

arXiv:cond-mat/0003161•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 2000•50 citations

SHORT-TIME CRITICAL DYNAMICS

Lothar Schülke

An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities. By a numerical simulation of the system one can measure the critical exponents and, by searching for the best power law behaviour, one can determine the critical point. Critical slowing down as well as finite size corrections are nearly absent, since the correlation length is still small for times far before equilibrium is reached. By measuring the (pseudo) critical points it is also possible to distinguish (weak) first-order from second-order phase transitions.

arXiv:hep-lat/0007003•International Workshop on Non-Perturbative Methods and Lattice QCD•Apr 1, 2001•0 citations

THE EXACT RENORMALIZATION GROUP AND FIRST-ORDER PHASE TRANSITIONS

N. Tetradis

Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields – the cubic anisotropy model. In the second part we review the application of the exact renormalization group to the calculation of bubble-nucleation rates. More specifically, we concentrate on the pre-exponential factor. We discuss the reliability of homogeneous nucleation theory that employs a saddle-point expansion around the critical bubble for the calculation of the nucleation rate.

arXiv:hep-th/0012107•International Journal of Modern Physics A•Apr 30, 2001•5 citations

New Numerical Method to Study Phase Transitions and its Applications

Jooyoung Lee

We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.

•Jan 1, 1991•0 citations

New numerical method to study phase transitions and its applications

Jooyoung Lee, J. Michael Kosterlitz

We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambigously a weak first order transition even when accessible system sizes are L/ξ<0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.

AIP conference proceedings•Jan 1, 1992•0 citations

Short-time dynamics of the 1D three-state long-range Potts model

Zvonko Glumac, Katarina Uzelac

We investigate the short-time dynamics of the one-dimensional q = 3 Potts model with a power-law decaying interactions of the form $r− (1+\sigma)$. This model is known to exhibit both first- and second-order transition regimes, which depend on the parameter of range $\sigma$ and are separated by a q-dependent tricritical point sigma_c(q) [1]. The location of this point, where the first-order transition becomes extremely weak presents difficulties both for RG approaches and for equilibrium numerical simulations [2-3]. We examine the first-order transition regime and its onset at sigma_c by dynamic Monte Carlo simulations, which recently appeared to be efficient in detecting weak first-order phase transitions [4]. We consider the short-time relaxation processes for magnetization and its higher momenta starting from high and low temperatures. We analyse the appearance of two pseudo critical temperatures characteristic for the first-order transition regime, which should merge at the tricritical point. [1] Z. Glumac and K. Uzelac, Phys. Rev. E 58, 4372 (1998) [2] E. Bayong, H. T. Diep, V. Dotsenko, Phys. Rev. Lett. 83, 14 (1999) ; K. Uzelac and Z. Glumac, Phys. Rev. Lett. 85, 5255 (2000) [3] Sylvain Reynal, Hung-The Diep, Phys. Rev. E 69, 026109 (2004) [4] L. Schuelke nad B. Zhang, Phys. Rev. E 62, 7482 (2000)

•Jul 13, 2007•0 citations
The dynamics of weak vs strong first order phase transitions is investigated numerically for (2 + 1)-dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition, with the order parameter being the equilibrium fractional population difference between the two phases at the critical temperature, and the control parameter being the coefficient of the cubic coupling in the free-energy density. The critical point is identified, and a power law controlling the relaxation dynamics at this point is obtained. Possible applications are briefly discussed.
An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities. By a numerical simulation of the system one can measure the critical exponents and, by searching for the best power law behaviour, one can determine the critical point. Critical slowing down as well as finite size corrections are nearly absent, since the correlation length is still small for times far before equilibrium is reached. By measuring the (pseudo) critical points it is also possible to distinguish (weak) first-order from second-order phase transitions.
Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields – the cubic anisotropy model. In the second part we review the application of the exact renormalization group to the calculation of bubble-nucleation rates. More specifically, we concentrate on the pre-exponential factor. We discuss the reliability of homogeneous nucleation theory that employs a saddle-point expansion around the critical bubble for the calculation of the nucleation rate.
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/{xi} < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambigously a weak first order transition even when accessible system sizes are L/ξ<0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems.
We investigate the short-time dynamics of the one-dimensional q = 3 Potts model with a power-law decaying interactions of the form r−(1+σ)r− (1+\sigma)r−(1+σ). This model is known to exhibit both first- and second-order transition regimes, which depend on the parameter of range σ\sigmaσ and are separated by a q-dependent tricritical point sigma_c(q) [1]. The location of this point, where the first-order transition becomes extremely weak presents difficulties both for RG approaches and for equilibrium numerical simulations [2-3]. We examine the first-order transition regime and its onset at sigma_c by dynamic Monte Carlo simulations, which recently appeared to be efficient in detecting weak first-order phase transitions [4]. We consider the short-time relaxation processes for magnetization and its higher momenta starting from high and low temperatures. We analyse the appearance of two pseudo critical temperatures characteristic for the first-order transition regime, which should merge at the tricritical point. [1] Z. Glumac and K. Uzelac, Phys. Rev. E 58, 4372 (1998) [2] E. Bayong, H. T. Diep, V. Dotsenko, Phys. Rev. Lett. 83, 14 (1999) ; K. Uzelac and Z. Glumac, Phys. Rev. Lett. 85, 5255 (2000) [3] Sylvain Reynal, Hung-The Diep, Phys. Rev. E 69, 026109 (2004) [4] L. Schuelke nad B. Zhang, Phys. Rev. E 62, 7482 (2000)