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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 modelPhysics Abstracts classification number: 0550

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The first-order phase transition in the three-state Potts model with long-range interactions decaying as 1/r 1+σ has been examined by numerical simulations using recently proposed Luijten-Blöte 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 σ was studied.

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 0, s i denotes a q-state Potts spin at the site i, δ is the Kronecker symbol and the summation is over

The phase diagram of the two- and three-state Potts model with infinite-range interactions in the external field is analyzed by studying the partition function zeros in the complex field plane. The tricritical point of the three-state model is observed as the approach of the zeros to the real axis at the nonzero field value. Different regimes, involving several first- and second-order transitions of the complicated phase diagram of the three-state model, are identified from the scaling properties of the zeros closest to the real axis. The critical exponents related to the tricritical point and the Yang-Lee edge singularity are well reproduced. Calculations are extended to the negative fields, where the exact implicit expression for the transition line is derived.

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