Random-field spin models beyond 1 loop: a mechanism for decreasing the lower critical dimension

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Field Theory

Background:

• The O(N) sigma model is a fundamental model in statistical mechanics and quantum field theory.
• Understanding phase transitions in disordered systems is crucial for materials science and complex systems.

Purpose of the Study:

• To investigate the ferromagnetic-disordered (F-D) transition in random-field and random-anisotropy O(N) sigma models.
• To determine the behavior of these models at different loop orders and in various dimensionalities.

Main Methods:

• Application of the functional renormalization group (FRG) technique.
• Analysis performed to the 2-loop level.
• Expansion in d = 4 + epsilon dimensions and at large N.

Main Results:

• Identified the F-D transition fixed point to the next order in d = 4 + epsilon for N > N(c).
• Found that for N < N(c), the lower critical dimension d(lc) drops below 4.
• Discovered two distinct fixed points for N < N(c), one for the quasiordered phase and a novel one for the F-D transition.
• Identified a glassy regime at large N.

Conclusions:

• The study provides a detailed understanding of phase transitions in disordered O(N) sigma models.
• The novel fixed point found for N < N(c) offers new insights into the nature of the F-D transition.
• The results are relevant for systems exhibiting quenched disorder and critical phenomena.