Models of Phase Transitions and Criticality

David A. Lavis, Roman Frigg

Oleg Borisenko, Gennaro Cortese, Roberto Fiore A +2 more

We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a cluster algorithm, valid for Z(N) models with odd values of N. The two-dimensional Z(5) vector model is conjectured to exhibit two phase transitions with a massless intermediate phase. We locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices and compare the results with analytical predictions.

Subeksha Bhattarai

The 2D Ising model is a simple yet powerful model to describe ferromag- netism. In this work, the phase transition and critical behavior of the 2D Ising model using the metropolis algorithm were investigated. Magnetization was an- alyzed as a function of temperature for lattice sizes L = 5, 10, 15, 20, 30. The analysis demonstrated a trend where the critical point becomes more sharply de- fined on increasing the lattice size. The value of the critical temperature obtained from the graph closely approximates the theoretical value. Hence, the simulation successfully demonstrated the phase transition of magnetic material from ordered to disordered state. The significance of Ising model further extends far beyond its application in understanding magnetism. This study provides a deeper under- standing of phase transition and critical behavior.

Subeksha Bhattarai

2D Ising model is simple yet powerful model to describe ferromagnetism. In this project, the phase transition and critical behaviour of the 2D Ising model using metropolis algorithm was investigated. The magnetisation vs temperature graph for different lattice size L = 5, L= 10, L = 15, L=20, L=30, was analyzed and compared. The analysis demonstrated a trend where the critical point becomes more sharply defined on increasing lattice size. The obtained value of critical temperature from graph closely approximates to the theoretical value. Hence the simulation successfully demonstrated the phase transition of magnetic material from ordered to disordered state. The significance of Ising model further extends far beyond its application in understanding magnetism. This study provides a deeper understanding of phase transition and critical behaviour.