By Michio Jimbo

This quantity often is the first reference ebook committed specifically to the Yang-Baxter equation. the topic pertains to large parts together with solvable types in statistical mechanics, factorized S matrices, quantum inverse scattering process, quantum teams, knot idea and conformal box idea. The articles assembled the following conceal significant works from the pioneering papers to classical Yang-Baxter equation, its quantization, number of recommendations, buildings and up to date generalizations to better genus suggestions.

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In this case some of the poles of the integrand of (E3 ) coincide and we find that (pf )efng = 7r-1 8 cos (m U) q2m In q, (E 12) which is proportional to (w2 - w3)2m In(w2 - w3 ). 2) are satisfied , in particular when w2 > w3 . The above equations also define an analytic continuation off across the w2 = w3 boundary, and we see that this function has a branch-point singularity. However, when w2 < w3 the true free energy is not given by the above equations. 5). 2 and w3 in these equations by a suffix 1.

181 of GR [8]) H(v) = 2iyg1/4 sinh(2a) 11 (1 - g2nZ)(l - g2nz l), n=1 (D11) Q(v) = y (1 - q2n-1z )( 1 fl n=1 - q2n lZ-1), 41 220 BAXTER where a, q, z are defined in terms of k and v by (D6) and (D8), and Y= n o - q2n). , r. , r. 12) implies that the integer v is zero and gives the exact equation Z1 ... Zr = (_ (D16) Or". 2) is an algebraic identity, valid for all complex values of v, and hence z. s . is dominated by a single term. 2) becomes r T(v) H (Z - Zj) N{( -1)r z1 ... Zrzr + lj. (D17) j=1 This equation is an identity , true for all values of z close to the unit circle .

3) will also be the same, provided neither spin o- nor spin o,,, lies inside the triangle ABC. 3) represents 64 equations. 6, so the 64 equations reduce to 16. 2. This means that there are only six distinct equations, namely cosh (K1+K2+K3+Ki -Kf -KZ) exp (2K +2Kk) = K cosh (-Ki+K,+Kk-Kti +K; +Kk) ( 4. 4) cosh (Ki - K; +Kk - Kz +K," +Kk) exp ( 2K - 2Kk) = cosh (Ki+K5-Kk-K,"+K +Kk) ( 4 . 5) where (i, j, k) is any permutation of (1, 2, 3). 5). 3) is then destroyed, leaving 16 apparently distinct equations.