Phase transitions in the Ising Model : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- Explain the meanings of the terms first order phase transition and continuous phase transition
- Explain how statistical mechanics shows that finite sized systems do not exhibit phase transitions
- Explain the meaning of the term thermodynamic limit
- Explain why the free energy of the Ising model is given by $F=-k_B T \ln \lambda_1$ in the thermodynamic limit. In this expression $\lambda_1$ is the principle eigenvalue of the transfer matrix
- Derive an expression for the average magnetisation of the Ising model in the thermodynamic limit
- Explain how the magnetic suceptibility is calculated and derive an expression for this quantity for the Ising model in the thermodynamic limit.
- Discuss the behavior of the suceptibility of the Ising model as the temperature goes to zero and whether or not this behavior is indivative of a phase transition.
- Explain the meanings of the terms first order phase transition and continuous phase transition
- Explain how statistical mechanics shows that finite sized systems do not exhibit phase transitions
- Explain the meaning of the term thermodynamic limit
- Explain why the free energy of the Ising model is given by $F=-k_B T \ln \lambda_1$ in the thermodynamic limit. In this expression $\lambda_1$ is the principle eigenvalue of the transfer matrix
- Derive an expression for the average magnetisation of the Ising model in the thermodynamic limit
- Explain how the magnetic suceptibility is calculated and derive an expression for this quantity for the Ising model in the thermodynamic limit.
- Discuss the behavior of the suceptibility of the Ising model as the temperature goes to zero and whether or not this behavior is indivative of a phase transition.