Special transitions in an O(n) loop model with an Ising-like constraint

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Lattice Models

Background:

• The O(n) nonintersecting loop model is a fundamental model in statistical mechanics.
• Understanding phase transitions and critical phenomena in lattice models is crucial for theoretical physics.

Purpose of the Study:

• To investigate the phase diagram of the O(n) nonintersecting loop model with a 90-degree bend constraint.
• To determine critical exponents and conformal anomalies for specific parameter ranges.
• To explore crossover phenomena to the generic O(n) universality class.

Main Methods:

• Transfer-matrix calculations were employed to analyze the model.
• Finite-size scaling techniques were used to determine critical behavior.
• The (x,z) phase diagram was explored for various loop weights (n).

Main Results:

• For 0
• For n>1, the O(n)-like transition is absent.
• A line of phase transitions exists for n≤1 when z=0, ending in an infinite-order transition at n=1.
• Critical exponents and conformal anomaly were determined along the n≤1 transition line.
• Crossover exponents to the generic O(n) universality class were calculated.

Conclusions:

• The results align with universal classifications for this type of model, particularly for -1≤n≤1.
• The study provides a detailed characterization of phase transitions and critical behavior in a constrained loop model.
• The introduction of topological defects offers a method to study crossovers between different universality classes.