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Landau theory
About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.
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TL;DR: The consequences of fluctuations about the mean field for the critical properties of a model with infinite-range interactions are examined and general scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.
Abstract: We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.
105 citations
105 citations
TL;DR: In this article, the authors used a general continuum model and utilize renormalization group and mean field theory methods to identify mechanisms that can lead to the experimentally observed charge density wave ordering.
Abstract: The newly discovered family of kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K,Cs,Rb) has recently gained wide attention. Here, the authors study these materials using a general continuum model and utilize renormalization group and mean field theory methods to identify mechanisms that can lead to the experimentally observed charge density wave ordering. The authors find that the charge density wave is the primary density wave instability in certain cases but could also be induced by a leading orbital current or spin density wave order.
104 citations
TL;DR: In this paper, the eigenvalue problems for the Ginzburg-Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions are studied.
Abstract: In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.
104 citations
TL;DR: In this article, the surface nucleation of superconductivity and the value of the upper critical field HC3 for superconductors occupying arbitrary bounded smooth domains in R3 were studied.
103 citations