Geometrical frustration and cluster spin glass with random graphs

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Magnetism

Background:

• Understanding cluster magnetism requires accounting for geometric frustration and disorder.
• Previous models often simplify the complex interplay between cluster geometry and network connectivity.
• The role of network connectivity in governing magnetic phases remains an active research area.

Purpose of the Study:

• To develop a theoretical framework for cluster magnetism incorporating geometric frustration and disorder.
• To investigate the influence of cluster network connectivity on magnetic phase transitions.
• To analyze the impact of different inner cluster geometries (triangular and tetrahedral) on magnetic ordering.

Main Methods:

• Development of a sparse random graph theory to model cluster networks.
• Application of replica theory and order parameter functions to analyze local field distributions.
• Consideration of uniform, antiferromagnetic intracluster interactions and Gaussian distributed intercluster interactions.
• Analysis of triangular and tetrahedral cluster geometries.

Main Results:

• For triangular clusters, a classical spin liquid state emerges at T*/J, followed by a cluster spin glass (CSG) phase at T/J.
• The CSG ground state in triangular clusters is robust against weak disorder and negative intracluster interactions, independent of network connectivity.
• Network connectivity significantly impacts frustration levels in triangular clusters with large J0/J.
• In contrast, the tetrahedral cluster geometry suppresses the CSG ground state under weak disorder or large negative J0/J.
• A reentrant CSG boundary phase, dependent on network connectivity, is observed for tetrahedral clusters.

Conclusions:

• The interplay of geometric frustration and disorder significantly influences cluster magnetism, with distinct behaviors observed for triangular and tetrahedral geometries.
• Network connectivity acts as a crucial parameter, modulating frustration and phase boundaries, particularly in non-frustrated systems.
• The developed theory provides a versatile tool for studying complex magnetic phenomena in disordered network systems.