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Critical behavior of the two-dimensional Ising susceptibility
W P Orrick1, B G Nickel, A J Guttmann
1Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia. worrick@ms.unimelb.edu.au
Physical Review Letters
|May 1, 2001
Summary
We computed short- and long-distance Ising susceptibility contributions using nonlinear equations. Scaling analysis revealed integer powers of tau, identifying irrelevant variable contributions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Ising model is a fundamental model in statistical mechanics used to study magnetism.
- Understanding susceptibility is crucial for characterizing phase transitions.
Purpose of the Study:
- To compute short- and long-distance contributions to the square-lattice Ising susceptibility.
- To analyze the scaling behavior near the critical temperature.
Main Methods:
- Summation of correlation functions using nonlinear partial difference equations.
- Analysis of high- and low-temperature series (N=323 terms) generated by an O(N^6) algorithm.
- Decomposition of susceptibility into short-distance and scaling contributions.
Main Results:
- Short-distance terms exhibit a specific power-law dependence on temperature (tau).
- The scaling part, after accounting for the leading singularity, shows integer powers of tau.
- Contributions of irrelevant variables were identified and quantified at leading orders (tau^(9/4) and tau^(17/4)).
Conclusions:
- The study provides detailed quantitative insights into the critical behavior of the square-lattice Ising model.
- The methods employed allow for the separation and analysis of different contributions to susceptibility.
- This work contributes to a deeper understanding of universality and scaling in critical phenomena.