• Corpus ID: 211066179

# Massless Phases for the Villain model in $d\geq 3$

@article{Dario2020MasslessPF,
title={Massless Phases for the Villain model in \$d\geq 3\$},
author={Paul Dario and Wei Wu},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 7 February 2020
• Mathematics
• arXiv: Mathematical Physics
We consider the classical Villain rotator model in $\mathbb{Z}^d, d\geq 3$ at sufficiently low temperature, and prove that the truncated two-point function decays asymptotically as $|x|^{2-d}$, with an algebraic rate of convergence. We also obtain the same asymptotic decay separately for the transversal two-point functions. This quantifies the spontaneous magnetization result for the Villain model at low temperature, and rigorously establishes the Gaussian spin-wave conjecture in dimension $d… 6 Citations ## Figures from this paper Depinning in the integer-valued Gaussian field and the BKT phase of the 2D Villain model • Mathematics • 2021 : It is shown that the Villain model of two-component spins over two dimensional lattices exhibits slow, non-summable, decay of correlations at any temperature at which the dual integer-valued Quantitative bounds on vortex fluctuations in$2d$Coulomb gas and maximum of the integer-valued Gaussian free field. • Physics • 2020 In this paper, we study the influence of the vortices on the fluctuations of$2d$systems such as the Coulomb gas, the Villain model or the integer-valued Gaussian free field. In the case of the$2d$Improved spin-wave estimate for Wilson loops in$U(1)$lattice gauge theory • Physics • 2021 In this paper, we obtain bounds on the Wilson loop expectations in 4D U(1) lattice gauge theory which quantify the effect of topological defects. In the case of a Villain interaction, by extending Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models • Mathematics • 2021 . For a family of integer-valued height functions deﬁned over the faces of planar graphs, we establish a relation between the probability of connection by level sets and the spin-spin correlations of The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature • Mathematics • 2022 The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integervalued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the Quantitative homogenization of interacting particle systems • Mathematics • 2020 For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are ## References SHOWING 1-10 OF 73 REFERENCES Existence Proof of a Nonconfining Phase in Four-Dimensional U(1) Lattice Gauge Theory A rigorous lower bound is obtained for the Wilson loop expectation value$〈A[C]〉$in the four-dimensional U(1) lattice gauge theory with an action of the Villain form. The bound, which holds for Massless phases and symmetry restoration in abelian gauge theories and spin systems • Mathematics • 1982 We give a new, elementary proof for the existence of a deconfining transition to a massless (QED) phase in the four-dimensionalU(1) lattice gauge theory and of an intermediate QED phase, accompanied Quantitative results on the corrector equation in stochastic homogenization • Mathematics • 2014 We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions$d\ge 2$. In previous works we studied the model problem of a discrete elliptic Fluctuations for the Ginzburg-Landau $${\nabla \phi}$$ Interface Model on a Bounded Domain We study the massless field on $${D_n = D \cap \tfrac{1}{n} \mathbf{Z}^2}$$, where $${D \subseteq \mathbf{R}^2}$$ is a bounded domain with smooth boundary, with Hamiltonian $${\mathcal {H}(h) = Cauchy-Born Rule from Microscopic Models with Non-convex Potentials • Mathematics • 2019 We study gradient field models on an integer lattice with non-convex interactions. These models emerge in distinct branches of physics and mathematics under various names. In particular, as zero-mass Green's function for elliptic systems: Moment bounds • Mathematics Networks Heterog. Media • 2018 The result implies optimal stochastic Gaussian bounds on the Green's function and its derivatives in the realm of homogenization of equations with random coefficient fields with finite range of dependence. Green’s function for elliptic systems: existence and Delmotte–Deuschel bounds • Mathematics • 2016 This paper is divided into two parts: In the main deterministic part, we prove that for an open domain$$D \subset \mathbb {R}^d$$D⊂Rd with$$d \ge 2$$d≥2, for every (measurable) uniformly elliptic Spontaneous symmetry breakdown in the abelian Higgs model • Physics • 1986 AbstractFor the abelian Higgs model we introduce a new gauge invariant observable which in Landau gauge is$$\phi (x)\bar \phi (y)$\$ . In three or more dimensions this observable is used to show that
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We prove that for low temperaturesT the spin-spin correlation function of the two-dimensional classicalSO(n)-symmetric Ising ferromagnet decays faster than |x|−constT providedn≧2. We also discuss a
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