The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r −(1+σ) has been studied in the wide range of parameters 0 < σ ≤ 1 and 1 16 ≤ q ≤ 64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented. Short title: Critical behaviour of the 1D LR q-state Potts model Recently, finite range scaling (FRS) appeared as an efficient method to deal with various discrete one-dimensional models with long range (LR) interactions (Glumac and Uzelac, 1989, 1991). The aim of the present study is to apply it to the onedimensional q-state Potts model with LR interactions, defined by the hamiltonianThe critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as r −(1+σ) has been studied in the wide range of parameters 0 < σ ≤ 1 and 1 16 ≤ q ≤ 64. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented. Short title: Critical behaviour of the 1D LR q-state Potts model Recently, finite range scaling (FRS) appeared as an efficient method to deal with various discrete one-dimensional models with long range (LR) interactions (Glumac and Uzelac, 1989, 1991). The aim of the present study is to apply it to the onedimensional q-state Potts model with LR interactions, defined by the hamiltonian

Jan 1, 199321 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)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, 20070 citations

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)