Titlebook: Statistical Approach to Quantum Field Theory; An Introduction Andreas Wipf Book 2021Latest edition The Editor(s) (if applicable) and The Au

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Monte Carlo Simulations in Quantum Mechanics,ill the workhorse in many simulations—the heat bath algorithm, and the hybrid Monte Carlo algorithm. We will apply these algorithms to simulate the anharmonic oscillator. Later in this book, we shall use these algorithms to analyze non-perturbative aspects of spin systems and quantum field theories.

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Scalar Fields at Zero and Finite Temperature,in quantum field theory. Even more important than their educational value is their role in the electroweak theory, where a scalar field interacts with the fields of leptons, quarks, and gauge bosons. The scalar field is needed for the Higgs mechanism which is essential to explain the mass generation

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Classical Spin Models: An Introduction,crete target space. The previously considered lattice scalar field theory with target space . defines a .. A typical representative of the class of . is the ubiquitous . and its generalizations. The target space of the Ising model is the finite group ... It is a simple statistical model for . induce

CLEFT

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High-Temperature and Low-Temperature Expansions,xpansions that suggested universality at criticality. Two expansions will be considered in this chapter. In the ., the Boltzmann factor is expanded in powers of the inverse temperature, and the sum over all configurations is taken term by term. In the Ising model, this leads to an expansion in power

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Peierls Argument and Duality Transformations,sing model by Onsager, Peierls (Proc Camb Phil Soc 32:471, 1936) proved the existence of two ordered phases at low temperatures. His argument can be extended to many other models with discrete target spaces. Here we present Peierls argument for the two- and three-dimensional Ising models.

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