Anisotropic Long-Range Spin Systems

TL;DR

This paper studies anisotropic long-range spin systems with direction-dependent decay exponents, revealing three regimes, phase diagrams, and critical exponents, with implications for physical systems exhibiting anisotropic interactions.

Contribution

It introduces a low energy effective action for anisotropic long-range interactions and characterizes the phase diagram and critical behavior across different regimes.

Findings

Identification of three regimes based on decay exponents

Derivation of phase diagram for anisotropic long-range systems

Estimation of critical exponents as functions of system parameters

Abstract

We consider anisotropic long-range interacting spin systems in $d$ dimensions. The interaction between the spins decays with the distance as a power law with different exponents in different directions: we consider an exponent $d_{1}+\sigma_1$ in $d_1$ directions and another exponent $d_{2}+\sigma_2$ in the remaining $d_2\equiv d-d_1$ ones. We introduce a low energy effective action with non analytic power of the momenta. As a function of the two exponents $\sigma_1$ and $\sigma_2$ we show the system to have three different regimes, two where it is actually anisotropic and one where the isotropy is finally restored. We determine the phase diagram and provide estimates of the critical exponents as a function of the parameters of the system, in particular considering the case of one of the two $\sigma$'s fixed and the other varying. A discussion of the physical relevance of our results is also presented.