The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K , whi...

It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simpl...

We consider the Taubes correspondencebetween solutions of the Seiberg– Witten equations on a compact 4-dimensional symplectic manifold and pseudoholomorphic curves on this manifold. We compare it with its 3-dimensional analogue in which the roles of Seiberg–Witten equations and pseudoholomorphic curves are played respectively by the Ginzburg–Landau equations and adiabatic paths in the moduli sp...

We prove the Landau–Ginzburg mirror symmetry conjecture between invertible quasihomogeneous polynomial singularities at all genera. That is, we show that FJRW theory (LG A-model) of such a is equivalent to Saito–Givental B-model) polynomial.

A large class of (0,2) Calabi-Yau σ-models and Landau-Ginzburg orbifolds are shown to arise as different “phases” of supersymmetric gauge theories. We find a phenomenon in the Landau-Ginzburg phase which may enable one to understand which Calabi-Yau σ-models evade destabilization by worldsheet instantons. Examples of (0,2) LandauGinzburg vacua are analyzed in detail, and several novel features ...