Abstract
In the last chapter, we showed that in many cases, the computation of properties of mechanical systems with many variables reduces to the evaluation of averages with respect to the canonical density \({e}^{-\beta H}/Z\). We now show how such calculations can be done, using the Ising model as an example.
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8.4. Bibliography
G. I. Barenblatt, Scaling, Cambridge University Press, Cambridge, 2003.
J. Binney, N. Dowrick, A. Fisher, and M. Newman, The Theory of Critical Phenomena, an Introduction to the Renormalization Group, the Clarendon Press, Oxford, 1992.
A.J. Chorin, Conditional expectations and renormalization, Multiscale Model. Simul., 1 (2003), pp. 105–118.
N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Perseus, Reading, MA, 1992.
J. Hammersley and D. Handscomb, Monte-Carlo Methods, Methuen, London, 1964.
G. Jona-Lasinio, The renormalization group—a probabilistic view, Nuovo Cimento, 26 (1975), pp. 99–118.
L. Kadanoff, Statistical Physics: Statics, Dynamics, and Renormalization, World Scientific, Singapore, 1999.
D. Kandel, E. Domany, and A. Brandt, Simulation without critical slowing down—Ising and 3-state Potts model, Phys. Rev. B 40 (1989), pp. 330–344.
J. Kominiarczuk, Acyclic sampling of Markov fields, with applications to spin systems, PhD thesis, UC Berkeley Mathematics Department, 2013.
J.S. Liu, Monte Carlo Strategies in Scientific Computing, Springer, NY, 2002.
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Chorin, A.J., Hald, O.H. (2013). Computational Statistical Mechanics. In: Stochastic Tools in Mathematics and Science. Texts in Applied Mathematics, vol 58. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6980-3_8
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DOI: https://doi.org/10.1007/978-1-4614-6980-3_8
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