Free energies and critical exponents of the ${A_1^{(1)}}$, $B_n^{(1)}$, $C_n^{(1)}$ and $D

Research Report MRR97-007

Free energies and critical exponents of the A₁⁽¹⁾, B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ face models

M.T. Batchelor, V. Fridkin, A. Kuniba, K. Sakai and Y.-K. Zhou

Abstract: We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation. The models considered are related to the affine Lie algebras $A_1^{(1)}$ , $B_n^{(1)},C_n^{(1)}$ and $D_n ^{(1)}$ . The bulk and surface specific heat exponents are seen to satisfy the scaling relation $2\alpha_s = \alpha_b + 2$ . It follows from scaling relations that in regime III the correlation length exponent $\nu$ is given by $\nu=(l+g)/2g$ , where l is the level and g is the dual Coxeter number. In regime II we find $\nu=(l+g)/2l$ .

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Free energies and critical exponents of the A1(1), Bn(1), Cn(1) and Dn(1) face models

M.T. Batchelor, V. Fridkin, A. Kuniba, K. Sakai and Y.-K. Zhou

Free energies and critical exponents of the A₁⁽¹⁾, B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ face models