Abstract
Critical and tricritical exponents for the two-dimensionalq-state Potts lattice gas are calculated using a Kadanoff lower-bound renormalization transformation with three variational parameters. The calculations support the picture proposed by Nienhuis et al. in which the critical and tricritical fixed points annihilate atq=4. For the most part, the exponents are in excellent agreement with the recent conjectures of den Nijs and of Nienhuis et al.
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Baxter, R.J.: J. Phys. C6, L445 (1973)
Potts, R.B.: Proc. Cambridge Philos. Soc.48, 106 (1952)
Nienhuis, B., Berker, A.N., Riedel, E.K., Schick, M.: Phys. Rev. Lett.43, 737 (1979)
Berker, A.N., Ostlund, S., Putnam, F.A.: Phys. Rev. B17, 3650 (1978)
Blume, M., Emery, V.J., Griffiths, R.B.: Phys. Rev. A4, 1071 (1971)
Niemeijer, T., van Leeuwen, J.M.J.: Phase Transitions and Critical Phenomena. Domb, C., Green, M.S. (eds.), vol. 6. London: Academic Press 1976
Berker, A.N., Wortis, M.: Phys. Rev. B14, 4946 (1976)
Nienhuis, B., Nauenberg, M.: Phys. Rev. Lett.35, 477 (1975)
den Nijs, M.P.M.: J. Phys. A12, 1857 (1979)
Baxter, R.J.: J. Phys. A13, L61 (1980)
Kadanoff, L.P., Brown, A.C.: Ann. Phys. (NY)121, 318 (1979)
Knops, H.J.F.: University of Nijmegen, preprint (1979)
Kadanoff, L.P.: Phys. Rev. Lett.34, 1005 (1975)
Kadanoff, L.P., Houghton, A., Yalabik, M.C.: J. Stat. Phys.14, 171 (1976)
Dasgupta, C.: Phys. Rev. B15, 3460 (1977)
den Nijs, M.P.M.: Physica A95, 449 (1979)
Nienhuis, B., Riedel, E.K., Schick, M.: J. Phys. A13, L31 (1980)
Burkhardt, T.W.: Phys. Rev. B13, 3187 (1976)
Knops, H.J.F.: Physica A86, 448 (1977)
Kadanoff, L.P., Houghton, A.: Phys. Rev. B11, 377 (1975)
Burkhardt, T.W.: Phys. Rev. B14, 1196 (1976)
Burkhardt, T.W., Knops, H.J.F.: Phys. Rev. B15, 1602 (1977)
den Nijs, M.P.M., Knops, H.J.F.: Physica A93, 441 (1978)
van Saarloos, W., van Leeuwen, J.M.J., Pruisken, A.M.M.: Physica A92, 323 (1978)
In the intervalq>1 the fixed-point free energy is maximized with respect toQ 2 and minimized with respect to exp [−4(Q 1+Q 3)] asQ 1+Q 3→∞ by the extremal variational parameters. On continuing toq<1, the maximum becomes a minimum and the minimum a maximum.
Hamer, C.J., Kogut, J.B., Susskind, L.: Phys. Rev. D19, 3091 (1979)
Hilhorst, H.J.: Phys. Rev. B16, 1253 (1977)
Flory, P.J.: Principles of Polymer Chemistry. Ithaca: Cornell Univ. Press 1953
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Burkhardt, T.W. Critical and tricritical exponents of the Potts lattice gas. Z. Physik B - Condensed Matter 39, 159–162 (1980). https://doi.org/10.1007/BF01301522
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DOI: https://doi.org/10.1007/BF01301522