Abstract
Series expansions remain, in many cases, one of the most accurate ways of estimating critical exponents. Historically it was the results from series expansions that suggested universality at criticality. Two expansions will be considered in this chapter. In the high-temperature series, 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 powers of \(\tanh (J/T)\ll 1\). In the low-temperature expansion, configurations are counted in order of their importance as the temperature is increased from zero. Starting from the ground state, the series is constructed by successively adding terms from 1, 2, 3, … flipped spins. In the Ising model, this leads to an expansion in powers of \(\exp (-2J/T)\ll 1\).
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Wipf, A. (2021). High-Temperature and Low-Temperature Expansions. In: Statistical Approach to Quantum Field Theory. Lecture Notes in Physics, vol 992. Springer, Cham. https://doi.org/10.1007/978-3-030-83263-6_9
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