Ising Model with First-, Second-, and Third-Neighbor Interactions

(m,d,N)=(1,3,2)Lifshitz point and the three-dimensionalButera1, Pernici2 2008Phys. Rev. B8061View full textAdd to dashboardCite

“…If, quite conservatively, we simply assume that α l is negative and |α l | < 0.1, we get from the hyperscaling law the rough bounds 0.36 < ν < 0.52, which are consistent with the O(ǫ 2 ) value ν ≃ 0.372 reported in table I. On the other hand, using the above reported estimate φ = 1.00(4) and the estimate β q = 0.40 (2) given below, we get the value ν = 0.40 (3). Plugging back this result into the hyperscaling law, we find the value α l = −0.01(6) for the specific-heat exponent, which is also compatible with all above indicated estimates.…”

“…As above remarked, the determination of the exponent α l from our series is not yet accurate enough to be useful. It does suggest, however, that α l = −0.02 (2), which is compatible with the ǫ-expansion estimate in Table I. If, quite conservatively, we simply assume that α l is negative and |α l | < 0.1, we get from the hyperscaling law the rough bounds 0.36 < ν < 0.52, which are consistent with the O(ǫ 2 ) value ν ≃ 0.372 reported in table I.…”

On the critical frontiers of Potts ferromagnets

“…The error introduced by the uncertainty on h cannot be seen within this scale. The same happens with the discrepancy (inferior to 0.3 % in the Si2) variables) between the results of references [24] (crosses in figure 4) and [25]. Once again we conjecture that this critical surface is valid Fig.…”

“…4. -The approximate para (P)-ferro (F) magnetic critical surface (heavy line) of the first-, second-and third-neighbour FCC lattice Ising model for 0 JZIJ1 2 and 0 J3/J, 2 which was obtained using Philhours' results [25] and h = 0.412 ± 0.026 (we have also indicated Dalton and Wood's values [24] ( x )). The dotted line is a guide-to-eye extrapolation which contains the correct limits for J2lJl --&#x3E; Co, J2lJ3 --&#x3E; oo (psc = 0.247 ± 0.003) and for J 3/J 1 ---+ oo, J3lJ2 ' 00 (we estimate pFcc(3) = 0.054 + 0.004).…”

“…As far as we know the critical surface for this lattice has been discussed only for q = 2. Philhours [25] has calculated the Ising transition temperatures for 0 J2/J1 2 and 0 J3IJ1 2, while Dalton and Wood [24] have considered only the particular case of firstand second-neighbour FCC lattice where 0 J2/J1 1 (J3J1 = 0). These results lead (for h = hFCC = 0.412 ± 0.026) to the critical surface shown in figure 4.…”