One-dimensional Ising model with long-range and random short-range interactions

TL;DR

This paper analyzes a one-dimensional Ising model with both long-range and random short-range interactions, revealing complex phase behavior including multiple tricritical points and various magnetic phases.

Contribution

It provides exact thermodynamic results for a generalized Ising model with mixed interactions, highlighting novel phase transitions and critical points.

Findings

Existence of a ferrimagnetic phase at low temperatures

Up to three tricritical points depending on interaction strength

Field-temperature diagrams with up to four critical points

Abstract

The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by Paladin et al. (J. Phys. I France 4, 1994, p. 1597). Exact results are obtained for the thermodynamic functions at arbitrary temperatures, and special attention is given to the induced and spontaneous magnetization. At low temperatures the system can exist in a ``ferrimagnetic'' phase with magnetization 0<m<1, in addition to the usual paramagnetic, ferromagnetic and antiferromagnetic phases. For a fixed distribution of the random variables the system presents up to three tricritical points for different intensities of the long-range interactions. Field-temperature diagrams can present up to four critical points.