arXiv subjects

D. A. Garanin

Publications and source records attributed to D. A. Garanin.

111 records · Page 7Linked to original sources

arXiv1998

Susceptibilities and Correlation Functions of the Anisotropic Spherical Model

The static transverse and longitudinal correlation functions (CF) of a 3-dimensional ferromagnet are calculated for the exactly solvable anisotropic spherical model (ASM) determined as the limit D \to \infty of the classical D-component vector model. The results are nonequivalent to those for the standard spherical model of Berlin and Kac even in the isotropic case. Whereas the transverse CF has the usual Ornstein-Zernike form for small wave vectors, the longitudinal CF shows a nontrivial behavior in the ordered region caused by spin-wave fluctuations. In particular, in the isotropic case below T_c one has S_{zz}(k) \propto 1/k (the result of the spin-wave theory) for k \lsim κ_m \propto T_c-T.

cond-mat.stat-mech↗

arXiv1998

Bloch-Wall Phase Transition in the Spherical Model

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D \to \infty. This exactly soluble model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T_B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T_B an additional anisotropy in the basis plane x,y is required; in purely uniaxial ferromagnets a domain wall behaves like a 2-dimensional system with a continuous spin symmetry and does not order into the Bloch one.

cond-mat.stat-mech↗

arXiv1998

The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field

The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical magnets described by the $D$-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the 1-st order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets χwith the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of χ(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0} χ(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0} χ(H,T)=1/(2|J_0|).

cond-mat.stat-mech↗