Tricriticality in Crossed Ising Chains

TL;DR

This paper investigates the phase diagram of a classical crossed Ising chain system, revealing complex critical behavior including tricritical points and confirming its universality class as 2D Ising.

Contribution

It introduces a detailed analysis of a crossed Ising chain model, identifying phase boundaries, tricritical points, and universality class through simulations and mean field theory.

Findings

Identification of four ordered phases and their boundaries.

Observation of tricritical points separating first and second order transitions.

Evidence that the model belongs to the 2D Ising universality class.

Abstract

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb$_{12}$O$_{29}$ and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we present evidence that this model belongs to the 2D Ising universality class.