Phase transitions are of great importance in a diversity of fields. They are usually classified into continuous phase transitions and first-order phase transitions (FOPTs). Whereas the former has a well-developed theoretical framework of the renormalization-group (RG) theory, no general theory has yet been developed for the latter that appear far more frequently. Focusing on the dynamics of a generic FOPT in the phi4 model below its critical point, we show by a field-theoretic RG method that it is governed by an unexpected unstable fixed point of the corresponding phi3 model. Accordingly, it exhibits a distinct scaling and universality behavior with unstable exponents different from the critical ones.

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We discuss how to extract the spectroscopy of quantum chromodynamics (QCD) in the pure gauge sector from the Hamiltonian lattice eld theory approach. The recently developed truncated eigenvalue equation method is applied to the estimation of the scalar glueball 0 ++ and 0 masses in the (2+1)-dimensional case. These masses reach the constant v alues in a scaling region as required by the renormalizability.