On the Phase Transition in a Model with Degenerate Minima

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where Q1 and Q, are real order parameters. We assume that constant a increases monotonically with temperature T and its sign is that of T ~ T 0, where T 0 is defined by a (T0) =0. Quantities c and k are positive constants. Quantity b is positive or negative constant, but b+c>O in order to guarantee the stability of system. Those three are considered to be independent of T for simplicity here. All the constants do not depend on the size of system, so that they are of the order of one. In the case b = 0 our model consists of two subsystems which are independent of and equivalent to one another. In the case b*O the third term in (1) couples the subsystems with one another. The whole system undergoes a phase transition of second order at T 0 , if we neglect the fluctuation of the order parameters. Let us discuss possible ordered states below To. Our free energy has quadruply degenerate minima. One finds two possible situations depending on the relative magnitudes of b and c. In case (I) where b>c>O the stable state is given by

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