Theory of Disorder (collective Pinning and Phase Transition)
Abstract
One weak force causes a weak distortion. The result of the action of many weak forces depends on a system: it may lead either to a weak or to a strong distortion. In the Abrikosov lattice of vortices in superconductors, the impurities (centers of pinning) are belonged to our laboratory system and do not move together with vortices. Therefore, the centers of pinning destroy the long-range order in the lattice. Short-range order exists only at the distance smaller than the correlation length L_c.[1] This results in appearance of a friction force, a critical current, a hysteresis. [2,3] In any business, it is important to have certain corner stones, meaning the results, which rise no doubts in their correctness. Such a corner stone for the physics of critical phenomena was provided by ONSAGER in 1944 by his exact solution of two dimensional Ising model. This paper stimulated a large number of theorists toward the study of critical phenomena. The methods of quantum field theory allowed to segregate the most divergent contributions of the perturbation theory: so called, parquet diagrams - and sum up these contributions. As the result, singularity close to phase transition in a real three dimensional system with dipole-dipole interaction was found exactly. [4] After obtaining the results, relevant to a real physical system, we completed this paper with two important appendices of a methodical character. In the first appendix we obtained the same result using the method of multiplicative renormalization group. This method is equivalent to that of parquet diagrams summation, but it is simpler and found later applications in different branches of condensed matter theory. In the second appendix we considered the effect of the symmetry of the order parameter on the singularity at the transition point in a non-physical four dimensional system. I am grateful to my co-authors Yu.N.Ovchinnikov and D.E.Khmelnitskii, my teachers A.D.Sakharov and A.B.Migdal. I should mention here the Landau Institute for Theoretical Physics, where these works were done. [1] A.I.Larkin, Sov. Phys. JETP 31, 784 (1970) [2] A.I.Larkin and Yu.N.Ovchinnikov, Sov. Phys. JETP 38, 854 (1974) [3] A.I.Larkin and Yu.N.Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979) [4] A.I.Larkin and D.E.Khmelnitskii, Sov. Phys. JETP 56, 2087 (1969)
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2002
- Bibcode:
- 2002APS..MAR.Q3001L