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Two-dimensional Ising model on random lattices with constant coordination number.

Manuel Schrauth¹, Julian A J Richter¹, Jefferson S E Portela^1,2

¹Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.

Physical Review. E

|March 18, 2018

Summary

Disordered two-dimensional Ising models exhibit varying critical exponents, suggesting no universal behavior. Lattice planarity and connectivity are crucial for stable phase transitions against topological disorder.

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Area of Science:

Statistical mechanics
Condensed matter physics
Network science

Background:

The two-dimensional Ising model is a fundamental model in statistical mechanics.
Understanding phase transitions in disordered systems is a key challenge.
Topological disorder, or variations in network connectivity, can significantly alter system behavior.

Purpose of the Study:

To investigate the impact of quenched topological disorder on the critical behavior of the two-dimensional Ising model.
To determine if universal critical exponents emerge in disordered lattices.
To explore the role of lattice planarity and connectedness in phase transition stability.

Main Methods:

Construction of random lattices with constant coordination number.
Large-scale Monte Carlo simulations.
Application of finite-size scaling relations to extract critical exponents.

Main Results:

Observed disorder-dependent effective critical exponents.
Found behavior analogous to diluted Ising models, indicating a lack of clear universality.
Results suggest topological disorder affects critical exponents.

Conclusions:

The phase transition in the two-dimensional Ising model is sensitive to quenched topological disorder.
Lattice planarity and connectedness are critical factors influencing the stability of phase transitions.
Universal behavior is not guaranteed in the presence of significant topological disorder.