A Dilute Ising Ferromagnet on a Hierarchical Lattice with Attractive Biquadratic Interactions

TL;DR

This study investigates a dilute Ising ferromagnet with annealed vacancies and attractive biquadratic interactions using renormalization group analysis on a hierarchical lattice, revealing phase diagrams, critical exponents, and basin interpretations.

Contribution

It introduces a detailed analysis of phase behavior and critical phenomena in a dilute Ising model with biquadratic interactions on a hierarchical lattice.

Findings

Phase diagrams as functions of temperature and vacancy concentration

Calculated critical exponents for phase transitions

Interpretation of basins of attraction in the renormalization group flow

Abstract

This paper considers a dilute Ising ferromangnet with annealed vacancies and attractive biquadratic interactions. Phase diagrams have been calculated while varying the temperature and concentration of annealed vacancies in the system while maintaining constant, attractive biquadratic couplings. These results have been produced using renormalization group analysis with a hierarchical lattice. Critical exponents have been calculated and each basin of attraction interpreted.