XY-Ashkin–Teller phase diagram in d=3

Alpar Türkoğlu and A. Nihat Berker

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

Abstract: The phase diagram of the Ashkin-Tellerized XY model in spatial dimension d=3 is calculated by renormalization-group theory. In this system, each site has two spins, each spin being an XY spin, that is having orientation continuously varying in 2π radians. Nearest-neighbor sites are coupled by two-spin and four-spin interactions. The phase diagram has ordered phases that are ferromagnetic and antiferromagnetic in each of the spins, and phases that are ferromagnetic and antiferromagnetic in the multiplicative spin variable. The phase diagram distinctively exhibits a pair of symmetrically situated direct bifurcation points and a pair of symmetrically situated reverse bifurcation points of the phase boundaries. The renormalization-group flows are in terms of the doubly composite Fourier coefficients of the exponentiated energy of nearest-neighbor spins.

Keywords: Doubled-up Ashkin–Teller complexity; Two continuously orientable spins per site; Double Fourier series renormalization group; Global phase diagram; Four different ordered phases; Reverse bifurcation points (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s037843712500367x

DOI: 10.1016/j.physa.2025.130715

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