arXiv:cond-mat/9807417 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

First-order transition in the one-dimensional three-state Potts model with long-range interactions

Zvonko Glumac, Katarina Uzelac

Published Oct 1, 1998• 18 citations

Abstract

The first-order phase transition in the three-state Potts model with long-range interactions decaying as ${1/r}^{1+\ensuremath{\sigma}}$ has been examined by numerical simulations using the recently proposed Luijten-Bl\"ote algorithm. By applying scaling arguments to the interface free energy, the Binder's fourth-order cumulant, and the specific heat maximum, the change in the character of the transition through variation of parameter \ensuremath{\sigma} was studied.

DOI: 10.1103/physreve.58.4372

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arXiv:cond-mat/9807417 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

First-order transition in the one-dimensional three-state Potts model with long-range interactions

Zvonko Glumac, Katarina Uzelac

Published Oct 1, 1998• 18 citations

arXiv HTML PDF

Abstract

The first-order phase transition in the three-state Potts model with long-range interactions decaying as

{1/r}^{1+\ensuremath{\sigma}}

has been examined by numerical simulations using the recently proposed Luijten-Bl"ote algorithm. By applying scaling arguments to the interface free energy, the Binder's fourth-order cumulant, and the specific heat maximum, the change in the character of the transition through variation of parameter \ensuremath{\sigma} was studied.

DOI: 10.1103/physreve.58.4372

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The first-order phase transition in the one-dimensional $q$ -state Potts model with long-range interactions decaying with distance as $1/r^{1+σ}$ has been studied by Monte Carlo numerical simulations for $0 < σ\le 1$ and integer values of $q > 2$ . On the basis of finite-size scaling analysis of interface free energy $ΔF_L$ , specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$ .The first-order phase transition in the one-dimensional $q$-state Potts model with long-range interactions decaying with distance as $1/r^{1+σ}$ has been studied by Monte Carlo numerical simulations for $0 < σ\le 1$ and integer values of $q > 2$. On the basis of finite-size scaling analysis of interface free energy $ΔF_L$, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$.

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The first-order phase transition in the three-state Potts model with long-range interactions decaying as

{1/r}^{1+\ensuremath{\sigma}}

First-order phase transition in

1d

Potts model with long-range interactions

The first-order phase transition in the one-dimensional

q

-state Potts model with long-range interactions decaying with distance as

1/r^{1+σ}

has been studied by Monte Carlo numerical simulations for

0 < σ\le 1

and integer values of

q > 2

. On the basis of finite-size scaling analysis of interface free energy

ΔF_L

, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for

σ

below a threshold value

σ_c(q)

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)