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Computer simulations often provide valuable insight into otherwise intractable problems. While the focus of modern physics is often theoretical, statistical mechanics is a cornerstone of many of modern physics' fundamental tools. Consequently, there is a continuing demand for efficient algorithms to perform computer simulations of quantum mechanical models defined on lattices. Most of the existing algorithms for performing classical statistical mechanics simulations are based a conventional Monte Carlo (MC) simulation framework. These algorithms suffer from a serious algorithmic problem; MC sampling becomes inefficient for systems that exhibit a phase transition between states. This work presented two types of algorithms that develop ingredients of multiscale systematic approaches: stochastic cluster simulations and multigrid Monte Carlo techniques. These algorithms significantly reduce the time and cost required to generate a statistical description of a model system and can be used efficiently for systems where conventional MC techniques become inefficient.

In this thesis we develop a multiscale framework for simulating lattice field theories. The key insight of the multiscale approach is that the complexity of a field theory is by no means localized but is spread over the full range of length scales. We introduce multiscale stochastic cluster Monte Carlo algorithms which are specifically designed to provide a statistical description of the large-scale dynamics of a field theory. The multiscale stochastic cluster algorithm uses a local microscopic description to predict the large scale behavior of the system, thereby removing the need for a coarse graining of the microscopic degrees of freedom.

The algorithmic scheme developed in this research is used to investigate the Euler-Klein-Gordon field as well as a toy model lattice scalar field theory. The latter case is used to validate the new multiscale Monte Carlo technique. We find that the ratio between the statistical fluctuations of the multiscale algorithm and the conventional MC method is significantly reduced. The resulting multiscale algorithm is also found to be up to three orders of magnitude faster than a standard MC simulation. d2c66b5586