Short-time dynamics in the 1D long-range Potts model

Abstract

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r 1+σ . The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents θ ′ and z are derived in the cases q = 2 and q = 3 for several values of the parameter σ belonging to the nontrivial critical regime. PACS. 05.50.+q Lattice theory and statistics -05.70.Jk Critical point phenomena -64.60.Ht Dynamic critical phenomena -61.20.Lc Time-dependent properties; relaxation 2 Model and short-time dynamics approach We consider the 1D Potts model defined by the Hamiltonian H = − i<j J |i − j| 1+σ δ si,sj ,where J > 0, s i denotes a q-state Potts spin at the site i, δ is the Kronecker symbol and the summation is over

Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

“…For these reasons, the study of relaxation processes in simple Ising and Potts models with LR interactions plays an important role for the understanding of the dynamics of second-order phase transitions. Within this context, the study of the short-time dynamics (STD) of critical systems has attracted great attention during the last two decades [1,[5][6][7], for a recent review see e.g. [8].…”

“…In fact, the field-theoretical calculations of Janssen et al [9] have been extended to the case of LR interactions decaying according to a power law for the case of the continuous n−vector model [1], the random Ising model [15], and the kinetic spherical model [16,17]. On the other hand, theoretical studies of the relaxation dynamics of discrete models are still lacking, and only few preliminary numerical results on the STD of the Potts model have recently been reported [7].…”

Investigating the nonequilibrium aspects of long-range Potts model: Refinement of critical temperatures and raw exponents

“…It is important to observe that β /ν = 0.102(1) does not agree with the conjecture used by [5] which, for σ = 0.7 is β /ν = (1 − σ )/2 = 0.15. Actually, we think that the conjecture must be true for q = 2 but not for q = 3.…”

“…Thus, by considering that 2β /ν = η (which is valid only to the twodimensional SR Potts model), we conclude that β /ν is equal to 1 − σ /2 instead of (1 − σ )/2 as used by the authors in Ref. [5] to obtain z through M x . Therefore, we think that the relation used by them was probably obtained otherwise and, as pointed out above, we think that it is not valid for LR systems.…”

“…Recently, Uzelac et. al [5] used the critical temperatures obtained in their previous works [4,3] to perform short-time MC simulations in order to present a preliminary study of the dynamic critical exponents θ and z of the Potts model with LR interactions described by the Hamiltonian given by Eq. ( 4) for the cases q = 2 and 3.…”