Phase transition of two-dimensional Ising models on the honeycomb and related lattices with striped random impurities

TL;DR

This paper investigates the phase transitions in 2D Ising models on honeycomb and square lattices with striped random impurities, deriving exact zero-temperature critical points and phase diagrams through numerical Lyapunov exponent calculations.

Contribution

It provides exact critical impurity fractions for phase transitions in these models and maps their phase diagrams using numerical methods.

Findings

Exact critical impurity fractions at T=0 for the models.

Phase diagrams showing transition lines in the p-T plane.

Numerical evaluation of Lyapunov exponents to determine phase boundaries.

Abstract

Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings have the same magnitude, exact critical values for the fraction p of ferromagnetic bonds at the zero-temperature (T=0) are obtained. The critical lines in the p-T plane are drawn by numerically evaluating the Lyapunov exponent of random matrix products.