Low-temperature behavior of the O(N) models below two dimensions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Field Theory

Background:

• O(N) models are fundamental in statistical mechanics and quantum field theory.
• Understanding critical behavior and low-temperature phases is crucial for characterizing materials and systems.

Purpose of the Study:

• Investigate critical behavior and low-temperature phases of O(N) models.
• Analyze the (d,N) plane, focusing on d≤2 and N≤2.
• Clarify the nature of order in low-dimensional systems.

Main Methods:

• Treating the number of field components (N) and dimension (d) as continuous variables.
• Utilizing Cardy-Hamber analysis for critical exponents.
• Employing nonperturbative renormalization group methods.

Main Results:

• Identified a region with algebraic correlation decay and a temperature-independent anomalous dimension (η).
• Demonstrated destabilization of long-range order in favor of quasi-long-range order for d<2 and N<2.
• Located low-temperature fixed points and observed their collision with critical fixed points near the lower critical dimension.

Conclusions:

• The study provides a precise charting of the (d,N) plane for O(N) models.
• Cardy-Hamber analysis and nonperturbative renormalization group methods show strong agreement in d<2.
• The findings offer new insights into critical phenomena and phase transitions in low-dimensional systems.