136 Progress of Theoretical Physics Supplement No. 157, 2005 Quasi Long Range Ordered Ground-State of the Random Field XY Model

We show that in the simple Imry-Ma type argument of random field XY model, ad-ditional vortex energy is missing which is crucial to explain the quasi-long-range ordered state experimentally observed in the so-called Bragg glass phase of superconductors. We also show numerical results which indicate that power-law correlated state is easily obtained by simple local relaxation scheme at zero-temperature. The same scheme is also applied to random field O(4) spin model, in which there are no topological defects, and we show that the obtained states have only short-ranged correlation. These results indicate that the topological defects are crucial in determining the low-temperature properties of random field spin models. The recent discovery of the “Bragg glass phase ” of dirty superconductors,1) in which translational order of the vortex-lattice shows power-law correlation, has been stimulating theoretical and numerical studies of relevant models. The random field XY model, as described below, is the most simple one among these models: H = −