TY - JOUR

T1 - Puzzle of bicriticality in the XXZ antiferromagnet

AU - Aharony, Amnon

AU - Entin-Wohlman, Ora

N1 - Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy Z axis has asymptotically either a tetracritical phase diagram or a triple point in the field-temperature plane. Neither experiments nor Monte Carlo simulations procure such phase diagrams. Instead, they find a bicritical phase diagram. Here, this discrepancy is resolved: After generalizing a ubiquitous condition identifying the tetracritical point, we employ different renormalization-group recursion relations near the isotropic fixed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the results from experiments and simulations can only be understood if their trajectories flow towards the fluctuation-driven first-order transition (and the associated triple point), but reach this limit only for prohibitively large system sizes or correlation lengths. In the crossover region one expects a bicritical phase diagram, as indeed is observed. A similar scenario may explain puzzling discrepancies between simulations and renormalization-group predictions for a variety of other phase diagrams with competing order parameters.

AB - Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy Z axis has asymptotically either a tetracritical phase diagram or a triple point in the field-temperature plane. Neither experiments nor Monte Carlo simulations procure such phase diagrams. Instead, they find a bicritical phase diagram. Here, this discrepancy is resolved: After generalizing a ubiquitous condition identifying the tetracritical point, we employ different renormalization-group recursion relations near the isotropic fixed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the results from experiments and simulations can only be understood if their trajectories flow towards the fluctuation-driven first-order transition (and the associated triple point), but reach this limit only for prohibitively large system sizes or correlation lengths. In the crossover region one expects a bicritical phase diagram, as indeed is observed. A similar scenario may explain puzzling discrepancies between simulations and renormalization-group predictions for a variety of other phase diagrams with competing order parameters.

UR - http://www.scopus.com/inward/record.url?scp=85139279914&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.106.094424

DO - 10.1103/PhysRevB.106.094424

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AN - SCOPUS:85139279914

SN - 2469-9950

VL - 106

JO - Physical Review B

JF - Physical Review B

IS - 9

M1 - 094424

ER -