Antiferromagnetic four-dimensional O(4) model

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We study the phase diagram of the four-dimensional O(4) model with first- (β_(1)) and second- (β2) neighbor couplings, especially in the β_(2) < 0 region, where we find a line of transitions which seems to be second order. We also compute the critical exponents on this line at the point β_(1) = 0 (F_(4) lattice) by finite-size scaling techniques up to a lattice size of 24, these exponents being different from the mean-field ones.
© 1997 The American Physical Society. The authors are grateful to J. L. Alonso, H. G. Ballesteros, V. Martín-Mayor, J. J. Ruiz-Lorenzo, C. L. Ullod, and D. Íñiguez for helpful discussions and comments. We thank especially J. M. Carmona for useful discussions concerning the logarithmic corrections. One of us (I.C.) wishes to thank R. D. Kenway for this kind hospitality at the Department of Physics and Astronomy, University of Edinburgh, as well as to Edinburgh Parallel Computing Center (EPCC) for computing facilities where part of these computations have been done under the financial support of TRACS-EC program. This work was partially supported by CICyT AEN95-1284, and AEN96-1670. I.C. thanks the Ministerio de Educación y Ciencia for financial support.
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