Transition to Classical Theory

Fan Zhong

Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only qualitatively accounted for by classical theories of nucleation, since their predictions often disagree with experiments by orders of magnitude. A theory to integrate FOPTs into the framework of the renormalization-group theory has been proposed but seems to contradict with extant wisdom. Here we show first that classical nucleation and growth theories alone cannot explain the FOPTs of the paradigmatic two-dimensional Ising model driven by linearly varying an externally applied field. Then we offer compelling evidence that the transitions agree well with the renormalization-group theory when logarithmic corrections are properly considered. This unifies the theories for both classes of transitions and FOPTs can be studied using universality and scaling similar to their continuous counterpart.

Mikhail Bespoyasov

This work introduces the State Locality Theory (SLT), a phenomenological framework describing the quantum–classical transition through a single continuous parameter of locality. The theory proposes that quantum behavior arises from low-locality states, while classical behavior emerges as locality increases, with decoherence interpreted as a natural consequence of this transition. SLT provides a unified explanation for interference visibility, gravitational amplification of locality, and the suppression of nonlocal correlations in macroscopic systems. The framework is formulated without modifying quantum mechanics, instead offering a phenomenological layer that clarifies how classicality emerges from quantum foundations. The theory outlines testable predictions, discusses implications for measurement, and proposes a structured approach for extending SLT toward a full dynamical formulation.

Stephen Powell, J. T. Chalker

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.