We study the critical behaviour of the -λφ ~4 + ηφ ~6 theory at finite chemical potential defined in a toroidal topology, with compactification of imaginary time (finite temperature) and compactification of a spatial coordinate. This is performed as an application of recently published methods for dealing with field theories defined on toroidal spaces. We study finite-size (described by the spatial compactification length L) and finite-chemical-potential (μ) effects, by carrying out an investigation of the critical temperature as a function of both L and μ. We find that there is a minimal size for the system that sustains the transition, and that this size is the same for all values of the chemical potential.
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