arXiv:1012.4251v1 [cond-mat.stat-mech] 20 Dec 2010 December 21, 2010 1:10 WSPC/INSTRUCTION FILE hff Modern Physics Letters B c  World Scientific Publishing Company PHASE TRANSITION IN HEISENBERG FULLY FRUSTRATED SIMPLE CUBIC LATTICE V. Thanh NGO *† and D. Tien HOANG ‡ Institute of Physics, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam H. T. DIEP §¶ Laboratoire de Physique Th´ eorique et Mod´ elisation, Universit´ e de Cergy-Pontoise, CNRS UMR 8089 2, Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. Received (Day Month Year) Revised (Day Month Year) The phase transition in frustrated spin systems is a fascinated subject in statistical physics. We show the result obtained by the Wang-Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple cubic lattice with the Heisenberg spin model. The degeneracy of the ground state of this system is infinite with two continuous parameters. We find a clear first-order transition in contradiction with previous studies which have shown a second-order transition with unusual critical properties. The robustness of our calculations allows us to conclude this issue putting an end to the 20-year long uncertainty. Keywords : Phase Transition; Classical Heisenberg Spin Model; Magnetism; Monte Carlo Simulation; Wang-Landau Method 1. Introduction During the last 30 years, intensive investigations have been carried out to study the effect of the frustration in spin systems. The frustration is known to be the origin of many unusual properties such as large ground state (GS) degeneracy, suc- cessive phase transitions, partially disordered phase, reentrance and disorder lines. Frustrated systems still constitute at present a challenge for theoretical physics. 1 One of the most studied aspects is the nature of the phase transition in frus- trated spin systems. Exact methods have been devised to solve with mathematical * nvthanh@iop.vast.ac.vn † Also at Division of Fusion and Convergence of Mathematical Sciences, National Institute for Mathematical Sciences, Daejeon, Republic of Korea. ‡ hdtien@iop.vast.ac.vn § diep@u-cergy.fr ¶ Corresponding author 1