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About the paper "METASTABLE STATES OF 2DIMENSIONAL ISOTROPIC FERROMAGNETS" A.A.Belavin, A.M.Polyakov JETP LETTERS 22, 245 (1975)
20140729 10:50:02
In Alexander Polyakov's and mine paper "Metastable States of 2Dimensional Isotropic Ferromagnets" [1], we have found metastable states of Heisenberg's ferromagnet. Such states now are called "instatons". The main reason for our search and discovery of such states was a hypothesis that such states would create an infinite correlation length at very low temperatures, obstructing spontaneous symmetry breaking. Later, this hypothesis was proven by calculation of partition function in the model using saddlepoint method, taking instantons into account. Actually, there was another reason for the search. The fact is that quantum theory of the field, which describes Heisenberg's 2dimensional ferromagnet, is in many ways similar to the YangMills theory. In the beginning of 1960s, GellMann has suggested that all elementary particles are made out of quarks. Since the beginning of 1970s, theoretical physicists have begun to assume that theory, which describes quark interaction, is YangMills theory. Experiments that were trying to study proton's structure have confirmed presence of quarks in them, but on the other hand, separately, quarks are not observed. This paradox is called color confinement. As G. 't Hooft has shown [2], quarks will not fly out, if YangMills theory has no spontaneous breaking of local calibration symmetry. In turn, an obstacle for such a breaking would be metastable states, instatons, if they appear in YangMills theory. Such states were later found in our work with Polyakov, Schwartz and Tyupkin [3]. [1] A.A. Belavin, A.M. Polyakov, JETP Letters 22, 245, (1975) [2] G. 't Hooft Nuclear Physics B 33, 173 (1971). [3] á.á. Belavin, á.í. Polyakov, á.S. Schwartz, Yu.S. Tyupkin, Phys.Lett. 59 B ,85 (1975) Download as PDF 