By R. Gobel

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D. Mukamel, Physical Review Letters, 34,482 (1975). 2. B. I. Halperin, T. C. Lubensky and S. K. Ma, Physical Review Letters, 32, 292 (1974). 3. S. Coleman and E. Weinberg, Physical Review, D7, 1888 (1973). 4. I. M. Gelfand and A. M. Yaglom, Journal of Mathematical Physics, 1, 48 (1960); E. J. 1967). See also the reviews by S. Albeverio and R. Hbegh-Krohn, Oslo University preprint ISBN-82-553-0193-3 (1974) and F. Guerra, L. Rosen and B. Simon, Annals of Mathematics, 101, 111 (1975). 5. H. Wagner, Zeitschrift f ?

Thus, if for some k , K ( k ) < 0 the matrix is not positive definite and our transformation (2-4 1) is undefined. Unfortunately, the matrix K for the king model always has negative eigenvalues, since all its diagonal elements are zero and thus the sum of its eigenvalues vanishes. 8 Since's = 1, we can add an arbitrary scalar matrix AZ t o J, and the energy changes by a trivial constant amount A - N . This trick, which is exact, makes the value of K O in (2-57) arbitrary. Also the connection with mean field theory becomes more problematic.

In the process our field @ acquires dimensions of length, [@I = L ’ (2-66) The representation of the theory in terms of continuous distributions in coordinate space is achieved by writing 1 &r) = -C exp(-ik f with I k I i k - r)@(k) (2-67) +p2$2] (2-68) < A, and then I d x Y o = ifdu[(V$)’ $(r) is not exactly @(ri),as a transform of the type (246) would have given. , F(@(ri))= Jka -d F[@(x)l (2-70) I The dimension of 6(r) can be evaluated either by using (2-66) and (2-69), or, 26 FIELD THEORY. THE RENORMALIZATION GROUP, A N D CRITICAL PHENOMENA which is a procedure independent of the contortions that we have undergone to reach (2-68), by noting that in the latter equation is dimensionless.