
Contents
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5.1 Sampling not summing 5.1 Sampling not summing
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5.2 Metropolis Monte Carlo 5.2 Metropolis Monte Carlo
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5.3 Trial moves in discrete space 5.3 Trial moves in discrete space
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5.4 Trial moves in continuous space 5.4 Trial moves in continuous space
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5.5 Ensemble reweighting 5.5 Ensemble reweighting
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5.6 Path integral Monte Carlo 5.6 Path integral Monte Carlo
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Further reading Further reading
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Additional exercises Additional exercises
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Cite
Abstract
In this chapter, we will focus exclusively on Monte Carlo approaches employed to study statistical mechanics of equilibrium systems. The basic idea of Monte Carlo is to estimate ensemble averages by sampling configurations from the Boltzmann distribution, which can be done by evolving the system using a stochastic process known as a Markov chain. In many cases, this can be done straightforwardly and the limitations of such an approach are only in the accuracy with which a system’s Hamiltonian is modeled, and the finite capacity of a computer that will restrict the system sizes and number of samples collected. Here, we will introduce both basic and more advanced algorithms, as well as discuss some practical aspects associated with simulating efficiently. We will render our presenta- tion concrete by considering a few paradigmatic models related to both classical and quantum mechanical systems.
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