Critical behavior of the two-dimensional Ising susceptibility

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.