The Transfer-Matrix Method (TMM) is a mathematical technique used primarily in statistical physics, condensed matter physics, and engineering to analyze the properties of one-dimensional systems such as spin chains, quantum systems, and wave propagation in stratified media. The method is particularly useful for studying systems that can be described in terms of discrete degrees of freedom arranged in a lattice.
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A method for counting or weighting configurations by processing successive slices and recording only the information that crosses the current boundary. Compatible boundary states define a matrix of transitions, so repeated slices can be handled by matrix powers. It is especially useful when the boundary is much smaller than the whole configuration.