Multiple transitions in an infinite range p-spin random crystal field Blume-Capel model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Spin Systems

Background:

• Investigating complex magnetic systems is crucial for understanding emergent phenomena.
• Spin-1 systems offer a richer playground for phase transitions compared to simpler spin-1/2 models.
• The influence of quenched disorder on phase transitions is a key area in statistical physics.

Purpose of the Study:

• To analyze the phase transitions in a p-spin model with ferromagnetic coupling and random crystal fields for spin-1 systems (p≥3).
• To explore the occurrence and characteristics of first-order transitions and Gardner-like transitions.
• To understand the system's behavior under varying strengths of random crystal fields and temperatures.

Main Methods:

• Theoretical analysis of a p-spin model with ferromagnetic interactions.
• Investigation of quenched random crystal fields with bimodal distribution.
• Examination of phase transitions at finite temperatures (T) and varying crystal field strengths (Δ).

Main Results:

• Identified lines of first-order transitions at finite T for all p≥3.
• Observed a triple point for weak Δ, and a critical point (Tc) for stronger Δ.
• Discovered a subsequent first-order transition upon increasing T from Tc, indicating a Gardner-like transition for finite p≥3.
• For p→∞, a single random first-order transition occurs only at T=0.

Conclusions:

• The p-spin model (p≥3) exhibits complex phase diagrams with first-order and Gardner-like transitions.
• The strength of the random crystal field significantly alters the nature and occurrence of these transitions.
• The model's behavior diverges for the infinite p limit, highlighting the importance of finite p effects.