  Switching interacting particle systems studied in probability theory are the
stochastic processes of hopping particles on a lattice made up of slow and fast
particles, where the switching between these types of particles occurs randomly
at a given transition rate. This paper explores how such stochastic processes
involving multiple particles can model group behaviors of ants. Recent
experimental research by the last author's group has investigated how ants
switch between two types of primarily relied cues to select foraging paths
based on the current situation. Here, we propose a discrete-time interacting
random walk model on a square lattice, incorporating two types of hopping
rules. Numerical simulation results demonstrate global changes in selected
homing paths, transitioning from trailing paths of the `pheromone road' to
nearly optimal paths depending on the switching parameters. By introducing two
types of order parameters characterizing the dependence of homing duration
distributions on switching parameters, we discuss these global changes as phase
transitions in ant path selections. We also study critical phenomena associated
with continuous phase transitions.
