Fazni prijelaz prvoga reda u 1d Pottsovom modelu s dugodosežnim međudjelovanjem

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 2. On the basis of thefinite-size scaling analysis of interface free energy ∆FL, specific heat and Binder’s fourth order cumulant, we obtain the first-order transition which occurs for σ below a threshold value σc (q ).U jednodimenzijskom Pottsovom modelu q–stanja s dugodosežnim međudjelovanjima koja opadaju s udaljenošću kao 1/r 1+σ , Monte Carlo simulacijama je promatran fazni prijelaz prvog reda za 0 2. Na temelju scaling analize slobodne energije međuplohe, specifične topline i Binderovog kumulanta četvrtog reda, dobivamo prijelaz prvoga reda za σ manji od granične vrijednosti σc(q)

Fazni prijelaz prvoga reda u 1d Pottsovom modelu s dugodosežnim međudjelovanjem

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 2. On the basis of thefinite-size scaling analysis of interface free energy ∆FL, specific heat and Binder’s fourth order cumulant, we obtain the first-order transition which occurs for σ below a threshold value σc (q ).U jednodimenzijskom Pottsovom modelu q–stanja s dugodosežnim međudjelovanjima koja opadaju s udaljenošću kao 1/r 1+σ , Monte Carlo simulacijama je promatran fazni prijelaz prvog reda za 0 2. Na temelju scaling analize slobodne energije međuplohe, specifične topline i Binderovog kumulanta četvrtog reda, dobivamo prijelaz prvoga reda za σ manji od granične vrijednosti σc(q)

Determination of the order of phase transitions in Potts model by the graph-weight approach

We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis of the shape of the graph-weight probability distribution. The approach is illustrated on special cases of the one-dimensional Potts model with long-range interactions and on its mean-field limit.Comment: 12 pages LaTeX, 2 eps figures; to be published in Physica

Critical behavior of the long-range Ising chain from the largest-cluster probability distribution

Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior in the non-classical critical regime corresponding to $0.5 <\sigma < 1$ is derived from the finite-size scaling analysis of the largest cluster.Comment: 4 pages, 2 figures, in RevTeX, to appear in Phys. Rev. E (Feb 2001

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

The first-order phase transition in the three-state Potts model with long-range interactions decaying as $1/r^{1+\sigma}$ has been examined by numerical simulations using 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 $\sigma$ was studied.Comment: 6 pages (containing 5 figures), to appear in Phys. Rev.

The critical behaviour of the long-range Potts chain from the largest cluster probability distribution

Abstract We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen-Wang cluster algorithm with cumulative probabilities. The ÿnite-size scaling analysis of the largest cluster is used to derive the critical behaviour in the non-classical regime of this model for various values of q. The models involving long-range interactions have an important role in describing many complex systems, from physics to economy or biology, but the equilibrium critical phenomena in these models are still not well understood and deserve further attention. We consider here the 1d Potts model with long-range interactions deÿned by the Hamiltonia