Upper critical dimension of the 3-state Potts model

Shai M. Chester; Ning Su

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arXiv · 2210.09091

Upper critical dimension of the 3-state Potts model

Shai M. Chester·Ning Su

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Abstract

We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal models, and so are exactly solvable. For $d>2$, however, strong coupling makes them difficult to study and there is no consensus on the value of $d_\text{crit}$. We use the numerical conformal bootstrap to compute critical exponents of both the critical and tricritical fixed points for general $d$. In $d=2$ our results match the expected values, and as we increase $d$ we find that the critical exponents of each fixed point get closer until they merge near $d_\text{crit}\lesssim 2.5$.

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Shai M. Chester, Ning Su. 2022-10-17. Upper critical dimension of the 3-state Potts model. https://arxiv.org/abs/2210.09091

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