Phase transitions in two-dimensional Z(N) vector models for N>4

Area of Science:

• Statistical physics
• Condensed matter theory
• Quantum field theory

Background:

• Renormalization group (RG) equations are crucial for understanding critical phenomena.
• Z(N) vector models provide a framework for studying phase transitions in various physical systems.

Purpose of the Study:

• To analytically and numerically investigate RG equations in 2D Z(N) vector models.
• To determine critical points and critical indices for phase transitions.
• To explore the scaling behavior of critical points with N.

Main Methods:

• Analytical investigation of renormalization group equations.
• Numerical analysis including Monte Carlo simulations.
• Computation of critical indices and analysis of helicity modulus behavior.

Main Results:

• The positions of critical points for two phase transitions in Z(N) vector models (N>4) were established.
• The critical index ν was computed.
• Monte Carlo simulations for N=7 and 17 located critical points and determined some critical indices.
• The behavior of the helicity modulus was studied for N=5, 7, and 17.

Conclusions:

• The study successfully established critical points and computed critical indices for 2D Z(N) vector models.
• Monte Carlo simulations validated analytical findings and provided further insights.
• The scaling of critical points with N was discussed, alongside open theoretical problems.