Phase transition in the n > 2 honeycomb O(n) model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Phase Transitions

Background:

• The O(n) loop model is a theoretical framework used to study phase transitions.
• Understanding the phase diagram of such models is crucial for various areas of physics.
• Previous research suggested no critical points for n>2 in this model.

Purpose of the Study:

• To determine the phase diagram of the O(n) loop model on the honeycomb lattice for n>2.
• To investigate the existence and nature of critical points in this parameter range.
• To explore the physical interpretations and universality classes of observed phase transitions.

Main Methods:

• Utilized the transfer-matrix method, a powerful technique for analyzing lattice models.
• Focused analysis on the specific case of the honeycomb lattice.
• Examined the behavior of the model in the range n>2.

Main Results:

• Identified a line of critical points for n between 2 and infinity.
• Found that this phase transition belongs to the three-state Potts universality class.
• Observed that the transition is unphysical for the O(n) spin model but physical for the n-component corner-cubic model.

Conclusions:

• The O(n) loop model exhibits unexpected critical behavior for n>2.
• The discovered phase transition offers new insights into universality classes and related physical systems.
• The findings can be interpreted in terms of soft particle ordering with hexagonal symmetry.