Spin-S Ising models with multispin interactions on the one-dimensional chain and two-dimensional square lattice

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Investigates spin-S Ising models, focusing on p-spin interactions.
• Examines the impact of varying spin magnitudes (S) and interaction orders (p) on magnetic systems.

Purpose of the Study:

• To analyze the effects of higher-order spin interactions on thermodynamic properties and phase transitions.
• To explore the dependence of free energy, spin-spin correlations, and phase transition characteristics on S and p.

Main Methods:

• One-dimensional model: Transfer matrix formulation and numerical diagonalization.
• Two-dimensional model: Multicanonical simulations.
• Analysis of order parameters, internal energy, specific heat, free energy, and spin-spin correlations.

Main Results:

• For S=1/2, free energy is independent of p, while correlations increase uniformly with p.
• For S≥1, free energy depends on p, and correlations significantly enhance at lower temperatures as p increases.
• Two-dimensional model exhibits first-order phase transitions for p≥3, strengthened by increasing p.

Conclusions:

• Higher-order interactions (p) critically affect spin correlations and phase transition properties.
• The nature and strength of phase transitions are modulated by both spin magnitude (S) and interaction order (p).