Ising model on directed small-world Voronoi Delaunay random lattices

TL;DR

This study explores the critical behavior of the Ising model on directed small-world lattices, revealing a second-order phase transition with unique critical exponents different from the regular 2D Ising model.

Contribution

It introduces the analysis of the Ising model on directed small-world lattices with quenched disorder, showing new universal critical exponents.

Findings

Disordered system does not belong to the same universality class as regular 2D Ising.

The model exhibits a second-order phase transition with p-independent critical exponents.

Critical exponents match those of the Ising and Blume-Capel models on directed small-world networks.

Abstract

We investigate the critical properties of the Ising model in two dimensions on {\it directed} small-world lattice with quenched connectivity disorder. The disordered system is simulated by applying the Monte Carlo update heat bath algorithm. We calculate the critical temperature, as well as the critical exponents $\gamma/\nu$, $\beta/\nu$, and $1/\nu$ for several values of the rewiring probability $p$. We find that this disorder system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The Ising model on {\it directed} small-world lattices presents in fact a second-order phase transition with new critical exponents which do not dependent of $p$, but are identical to the exponents of the Ising model and the spin-1 Blume-Capel model on {\it directed} small-world network.