On the Residual Entropy of the Blume-Emery-Griffiths Model |
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Authors: | Gastão A Braga Paulo C Lima |
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Institution: | (1) Departamento de Matemática, UFMG, Caixa Postal 1621, 30161-970 Belo Horizonte, MG, Brazil |
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Abstract: | By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered
phase boundaries satisfies the inequalities (ln λ
1,n
)/(n+1)≤S≤(ln λ
1,n
)/n, where λ
1,n
is the largest eigenvalue of a transfer matrix F
n
on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ
1,n
)/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors. |
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Keywords: | Residual entropy Blume-Emery-Griffiths model Transfer matrix |
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