Phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field

Abstract

The phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field in two dimensions is explored by renormalization group, conventional finite-size scaling, and conformal invariance techniques. We found that the phase diagram of this model is qualitatively the same as that of the dilute 4-states Potts model, presenting a multicritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. However, our results indicate that the critical exponents vary continuously along the second-order transition line, differently from the expected behavior of the dilute 4-states Potts model.

Monte Carlo study of the spin-1 Baxter-Wu model

“…In addition, as we have shown, a second-order phase transition takes place at D = 0 in contrast with the conjecture that the spin-1 Baxter-Wu model is critical only in the limit D → −∞ [13]. Some preliminary results, agreeing with the picture of a line of second-order phase transition with varying exponents and the presence of a multicritical point, for the present system with crystal field interaction, have already been obtained from conformal invariance with finite-size scaling theory and the mean field renormalization group approach [14]. Work in this direction using Monte Carlo simulations is now in progress.…”

Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field

“…For the spin-1 model, within our computational power, we can consider strip widths up to L = 12, while for spin-3/2 we were limited to L = 9. As we could increase the size of the system further when compared to the previous work (L = 9) [21] for spin-1, we have revisited this model in order to seek the difference it makes to consider an additional larger strip and to obtain the correlation length exponent given directly from Eq. (6) as well, where the latter quantity was not exploited in the previous study.…”

“…Regarding the first-order transition line, a finite-size estimate can be obtained by the same procedure as done in recent works [18,21]. Along the first-order transition line of the Baxter-Wu model with a crystal field, we have the coexistence of p phases.…”

“…These authors interpreted the changes of the estimated thermal exponents 1/ν along the transition line as a signal that a second-order transition should happen only for D → −∞ (the pure Baxter-Wu model). Nevertheless, more recently [21], renormalization-group, conventional finite-size scaling, and conformal invariance techniques have been applied to the spin-1 Baxter-Wu model and the presence of a multicritical point has in fact been achieved.…”

Αλλαγές φάσης στο πρότυπο Baxter-Wu

“…Με βάση τα προαναφερθέντα, ισχυριζόμαστε [6] ότι το κρίσιμο σημείο (0, T c ) συμπεριφέρεται σαν απωστικό κρίσιμο σημείο (irrelevant critical point) ενώ θα πρέπει να υπάρχει και ένα άλλο κρίσιμο σημείο, ίσως το (−6J, 0), το οποίο θα συμπεριφέρεται σαν ελκτικό (relevant). Εξίσου πιθανή είναι και η παρουσία ενός τρίτου πολυκρίσιμου σημείου (multicritical point) κατά μήκος αυτής της φασικής γραμμής, όπως είναι γνωστό ότι συμβαίνει τόσο στο μοντέλο των Blume-Capel όσο και στο spin-1 πρότυπο Baxter-Wu παρουσία κρυσταλλικού πεδίου ( [114], [115]). Υυσικά, τα παραπάνω συνιστούν ζητήματα προς επιστημονική διερεύνηση, πλην όμως η παρουσία ενός ακόμα κρίσιμου σημείου θα μπορούσε σίγουρα να θεωρηθεί εναλλακτική λύση σε σχέση με την ύπαρξη συνεχούς γραμμής από το σημείο (0, T c ) μέχρι το σημείο (−6J, 0).…”