Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices

TL;DR

This study investigates the critical behavior of the spin-1 Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay lattices, revealing different universality classes and phase transition types depending on lattice directionality and rewiring probability.

Contribution

It provides the first analysis of the Blume-Capel model on these complex lattices, showing how connectivity disorder affects phase transitions and universality classes.

Findings

Undirected lattices share universality class with regular 2D model.

Directed lattices exhibit second-order or first-order transitions depending on q.

Critical exponents differ from the regular 2D ferromagnetic model for q < qc.

Abstract

The critical properties of the spin-1 two-dimensional Blume-Capel model on directed and undi- rected random lattices with quenched connectivity disorder is studied through Monte Carlo simulations. The critical temperature, as well as the critical point exponents are obtained. For the undi- rected case this random system belongs to the same universality class as the regular two-dimensional model. However, for the directed random lattice one has a second-order phase transition for q < qc and a first-order phase transition for q > qc, where qc is the critical rewiring probability. The critical exponents for q < qc was calculated and they do not belong to the same universality class as the regular two-dimensional ferromagnetic model.