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Correlation Functions, Universal Ratios and goldstone mode singularities.in n-Vector models

Communications in Computational Physics 2014年第5期15卷 1407-1430页

作者： J.Kaupuzs R.V.N.Melnik J.Rimsans Institute of Mathematics and Computer Science University of Latvia29 Rai¸na BoulevardLV1459RigaLatvia Institute of Mathematical Sciences and Information Technologies University of Liepaja14 Liela StreetLiepaja LV-3401Latvia Wilfrid Laurier University WaterlooOntarioCanadaN2L 3C5.

Correlation functions in the O(n)models below the critical temperature are *** on Monte Carlo(MC)data,we confirm the fact stated earlier by Engels and Vogt,that the transverse two-plane correlation function of the O(4)model for lattice sizes about L=120 and small external fields h is very well described by a Gaussian ***,we show that fits of not lower quality are provided by certain non-Gaussian *** have also tested larger lattice sizes,up to L=*** Fourier-transformed transverse and longitudinal two-point correlation functions have goldstone mode singularities.in the thermodynamic limit at k→0 and h=+0,i.e.,G_(⊥)(k)≈ak−λ_(⊥)and G_(||)(k)≈bk−λk,*** a and b are the amplitudes,k=|k|is the magnitude of the wave vector *** exponentsλ_(⊥),λk and the ratio bM^(2)/a^(2),where M is the spontaneous magnetization,are universal according to the GFD(grouping of Feynman diagrams)*** we find that the universality follows also from the standard(Gaussian)theory,yielding bM^(2)/a^(2)=(n−1)/*** MC estimates of this ratio are 0.06±0.01 for n=2,0.17±0.01 for n=4 and 0.498±0.010 for n=*** to these and our earlier MC results,the asymptotic behavior and goldstone mode singularities.are not exactly described by the standard *** is expected from the GFD *** have found appropriate analytic approximations for G_(⊥)(k)and G_(||)(k),well fitting the simulation data for small *** have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately。

关键词： n-component vector models correlation functions Monte Carlo simulation goldstone mode singularities.

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