Effect of Field Direction and Field Intensity on Directed Spiral Percolation

TL;DR

This study investigates how the direction and strength of external bias fields influence the critical behavior of directed spiral percolation in two dimensions, revealing a new universality class and a phase diagram of model transitions.

Contribution

It introduces a detailed numerical analysis of DSP under varying field directions and intensities, identifying a new universality class and mapping phase transitions.

Findings

DSP belongs to a new universality class distinct from other percolation models.

The universality class remains unchanged with variations in the $E$ field direction.

A phase diagram illustrating transitions between DSP and other models based on field intensities.

Abstract

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field ($E$) and a field of rotational nature ($B$) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of $E$ field and intensities of both $E$ and $B$ fields in 2 dimensions. The system shows interesting and unusual critical behaviour at the percolation threshold. Not only the universality class of DSP model is found to belong in a new universality class than that of other percolation models but also the universality class remains invariant under the variation of $E$ field direction. Varying the intensities of the $E$ and $B$ fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields $E$ and $B$.