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Foundations of Statistical Mechanics
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Module 10
Exact Solutions and Correlation Functions
1
Solving the 1D Ising Model with the Transfer Matrix Method
Solve the 1D Ising model in zero field exactly using the transfer matrix method.
2
1D Ising Model: Transfer Matrix Method
Compute the free energy, magnetization, and susceptibility for the 1D Ising model from the transfer matrix eigenvalues.
3
Spin-Spin Correlation in the 1D Ising Model
Define the spin-spin correlation function and compute the correlation length for the 1D Ising model.
4
1D Ising Model: No Phase Transition
Explain why the 1D Ising model has no finite-temperature phase transition, both from the exact solution and via a domain-wall entropy argument.
5
Correlation Length: 1D vs. Mean-Field
Contrast the behavior of the correlation length in the 1D model with the mean-field prediction for higher dimensions.
Previous module
Interacting Systems and Mean-Field Theory
Next module
Phase Transitions and Critical Phenomena