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Updated: Jun 14, 2026
05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Specific heat of the simple-cubic Ising model
1College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, 29 Yudao St, 210016 Nanjing, People's Republic of China.
Summary
We developed a quantitative expression for the Ising model's specific heat near its critical point. This formula, derived from Monte Carlo simulations, accurately predicts critical phenomena and universal amplitude ratios.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Ising model is a fundamental model in statistical mechanics for studying magnetism and phase transitions.
- Understanding critical phenomena, such as specific heat divergence, is crucial for characterizing phase transitions.
Purpose of the Study:
- To derive a quantitative expression for the specific heat of the Ising model in the critical region.
- To determine the universal amplitude ratio of specific heat divergences.
Main Methods:
- Finite-size scaling analysis of numerical data.
- Monte Carlo simulations on a simple-cubic lattice.
Main Results:
- A quantitative expression for specific heat in the critical region was established.
- The expression shows satisfactory agreement with series expansions and experimental data.
- The universal amplitude ratio of specific heat divergences was determined.
Conclusions:
- The derived expression accurately describes the specific heat behavior of the Ising model near criticality.
- The study provides insights into critical phenomena and validates theoretical models with numerical and experimental findings.
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