1994/02/23 by G. Ramirez-Santiago, Guillermo Ramı́rez-Santiago, Jorge V. José · 87 citations
Physics and Astronomy · #Classical XY model #Condensed matter physics #Critical exponent #Frustration #Ising model #Lattice (music) #Mathematical physics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevb.49.9567
published in Physical review. B, Condensed matter 49(14), 9567-9582 (American Physical Society) · 47 pages (PHYZZX)
arxiv created 1994/02/23 · openalex publication_date 1994/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We present a detailed study of the critical properties of the two-dimensional (2D) XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge-invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to 240\ifmmode×\else\texttimes\fi240; the chiral correlation functions are studied on lattices up to 96\ifmmode×\else\texttimes\fi96. We find that the critical exponents of the spin-phase transition are \ensuremathν=0.3069 and \ensuremathη=0.1915, which are to be compared with the unfrustrated XY model exponents \ensuremathν=1/2 and \ensuremathη=0.25. We also find that the critical exponents of the chiral transition are \ensuremathν_\mathrm\ensuremathχ=0.875, 2\ensuremathβ=0.1936, 2\ensuremathγ=1.82, and 2\ensuremathγ'=1.025, which are different from the expected 2D Ising critical exponents. The spin-phase transition occurs at TU(1)=0.446, which is about 7% above the estimated chiral critical temperature TZ2=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.