Critical Phenomena in Phase Transformation and Fractals

Introduction to Phase Transitions and Critical Phenomena

Critical phenomena and noise-induced phase transitions in neuronal networks.

We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of s...

Critical Point Phenomena and Phase Transitions in the Ising Model

A Monte Carlo simulation of the Ising Model, a simplified model for studying the behavior of magnetic materials at various temperatures, was constructed. This model illustrated the transition between magnetic and non-magnetic phases as temperature is increased, and showed critical-point behavior at the transition. A general system for studying the behavior of many different configurations of pa...

Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States

This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, fieldtheoretic aspects, numerical tec...

Phase Transitions, Critical Phenomena and Exactly Solvable Lattice Models

An overview is given of the study of phase transitions and critical phenomena in statistical mechanics with an emphasis on the general principle of universality and the role of spatial dimension and symmetry in determining critical behaviour. Although we live in three dimensions, our most complete understanding of critical behaviour is in two dimensions. This circumstance results from the remar...