Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process

TL;DR

This paper introduces a universal field theoretic model for multi-species directed percolation, revealing that near extinction thresholds, the system exhibits universal critical behavior and tends toward species differentiation due to an inherent instability.

Contribution

It develops a comprehensive field theoretic framework for multi-species directed percolation, demonstrating universal critical exponents and an instability causing species differentiation.

Findings

Universal critical exponents match Reggeon field theory

Model exhibits instability leading to species asymmetry

Near extinction, behavior is governed by well-known exponents

Abstract

A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well known exponents of Reggeon field theory. In addition this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.