Tricriticality in Crossed Ising Chains

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.

References in corpus (4)

• Unconventional Bose-Einstein Condensations Beyond the "No-node" Theorem
• Exact Solution of Ising Model on a Small-World Network
• Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices
• Organometallic-like localization of 4d-derived spins in an inorganic conducting niobium suboxide

Cited by in corpus (1)

• Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents