Mirror theory of spin systems with a surface

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The authors discuss the mirror theory of spin systems with a surface. In the semi-infinite system, the 2-point correlation function at bulk critical temperature depends only on the 'real' distance and the 'image' distance, as was shown by the present authors within the framework of 1/n expansion and more recently by Cardy with the use of the conformal invariance. According to this mirror theory, they directly show the scaling relation 2 eta perpendicular to - eta /sub /// eta . They also find a universal combination of amplitudes. They check the mirror theory by means of the epsilon (=4-d) expansion and present the explicit form of the correlation function in real space up to O( epsilon 2). The resulting surface critical exponents eta perpendicular to and eta /sub /// coincide with those obtained previously.

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