First-order phase transition in $1d$ Potts model with long-range interactions

Abstract

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&#39;s fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$.