Multigrid Monte Carlo method. IV. One-dimensional O(4)-symmetric nonlinear σ model

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 53, Issue 6, 1996, Pages 3438-3444

  Mendes, Tereza ^a   Sokal, Alan D ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039366050     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.53.3438     Document Type: Article

References (31)

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27. Confidence level is the probability that the chi (formula presented) would equal or exceed the observed value, assuming that the underlying statistical model (“null hypothesis”) is correct.
28. Our preceding results suggest that we ought to use instead a logarithmic ansatz: e.g., [ τ, A (β, L) approx [ln ξ (β, L) + c (ξ (β, L) / L bbox) ] g-A bbox(ξ (β, L) / L bbox) . ] But it is difficult to know what to use for the function c (ξ (β, L) / L bbox). If one simply uses c equiv 0, the agreement is poor; clearly the additive constant cannot be neglected for our range of L, as is obvious already from Figs. reffig1 and reffig3 and Table reftab3. So we decided to use instead the power law ansatz as a reasonable “phenomenological” fit.
29. It is of course equivalent to use the ansatz [ τ -int, A (β, L) sim (formula presented) -int, A) hat g -A bbox(ξ (β, L) / L bbox), ] and indeed the two ansätze are related by hat g (formula presented) (x). However, to determine whether lim (formula presented) hat (formula presented) (x) is nonzero, it is more convenient to inspect a graph of (formula presented) than one of hat g (formula presented).
30. Note that, contrary to much belief, τ (formula presented) =0. For further discussion, see cite1,4.
31. All three criteria translate, in different ways, the intuitive idea of using the largest t such that the signal to noise ratio is “not too small.” In particular, criterion (c) comes from the fact that the statistical error bar on ρ (formula presented) (t) is roughly of order [τ (formula presented): see cite1,23,24,25.