Phase transitions in XY models with randomly oriented crystal fields.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Disordered Systems

Background:

• The XY model is a fundamental model in statistical mechanics, often used to study phase transitions.
• Understanding the effects of quenched disorder on magnetic systems is crucial for materials science.

Purpose of the Study:

• To investigate the free energy of an XY model with random crystal fields.
• To determine the impact of disorder distribution and strength on critical temperature and specific heat.
• To map the phase diagram under asymmetric disorder conditions.

Main Methods:

• Large deviation theory applied to an arbitrary probability distribution of disorder.
• Analysis of the XY model on a fully connected graph.
• Investigation of specific heat behavior at low temperatures.
• Determination of the phase diagram for asymmetric bimodal distributions.

Main Results:

• The critical temperature is insensitive to the nature and strength of the random orientation distribution for a broad class of distributions.
• Specific heat vanishes as temperature approaches zero for infinite crystal field strength (D→∞), but approaches a constant for finite D.
• A phase diagram with four phases (mixed, x-Ising, y-Ising, paramagnetic) meeting at a tetracritical point was identified.
• A canted mixed phase exists for finite D and disappears as D approaches infinity.

Conclusions:

• The critical temperature of the XY model exhibits remarkable robustness against variations in random crystal field orientation distributions.
• The interplay between crystal field strength and disorder leads to distinct low-temperature behaviors and complex phase diagrams.
• Asymmetric disorder introduces new phases and critical points, enriching the understanding of magnetic systems with quenched disorder.