Landau theory

About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.

Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

Abstract: Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10^{-9}. Our study establishes the existence of two strain thresholds, the first, epsilon_L, below which the material is essentially linear, and the second, epsilon_M, below which the material is nonlinear but where quasiequilibrium thermodynamics still applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above epsilon_M the behavior becomes truly nonequilibrium -- as demonstrated by the existence of material conditioning -- and Landau theory no longer applies. The main focus of this paper is the study of the region below the second threshold, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

Jahn-Teller induced phase transition in CsCuCl3: structural phase transition with helical atomic displacements

Abstract: The 423K phase transition of CsCuCl3 is attributed to a cooperative Jahn-Teller effect. Using results of the group-theoretical analysis of phonon modes, it is shown that helical atomic displacements in the low-temperature phase can be represented by a suitable linear combination of the polarization vectors of the Jahn-Teller active E1 modes with wavevectors q=+or-(0 0 2 pi /3c) of the high-temperature phase. The transition may be regarded as an order-disorder limit of the pseudospin-phonon coupled-type phase transition. Formation of the helical structure through the first-order transition is explained on the basis of the group-theoretical formulation of the Landau theory of phase transitions.

Ferromagnetic Transitions and the One‐Third‐Power Law

Abstract: Experiments have shown that the reduced magnetization of insulating ferromagnets varies as m(T) = D(1‐T/Tc)f for T>0.9Tc, and that f=⅓. We report calculations of the magnetization of the Heisenberg model which give, over a wide temperature range, both the observed exponent f=⅓ and the observed co‐efficient D, within 2% of the experimental value. This result is obtained for a two‐spin cluster theory; similar but slightly less satisfactory agreement is demonstrated by two forms of Green function theory. Because these theories are not satisfactory in the immediate vicinity of the phase transition, and because the experimental ⅓‐power law extends far from the transition [in terms of m(T)], we suggest that the ⅓‐power law may be a property of the stable ferromagnetic phase rather than a reflection of the phase transition in the sense of the Landau theory.

Existence of Partially Regular Solutions for Landau–Lifshitz Equations in ℝ3

Abstract: We establish the existence of partially regular weak solutions for the Landau–Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based on Ginzburg–Landau approximation. The new key ingredient is a nonlocal representation formula for the penalty term that permits us to take advantage of the special trilinear structure of the limiting nonlinearity.