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Field-theory results for three-dimensional transitions with complex symmetries

Pasquale Calabrese·Andrea Pelissetto·Paolo Rossi·Ettore Vicari
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Abstract

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $ϕ^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $ε$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.

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Pasquale Calabrese, Andrea Pelissetto, Paolo Rossi, Ettore Vicari. 2002-12-13. Field-theory results for three-dimensional transitions with complex symmetries. https://doi.org/10.1142/s0217979203023355

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