Upper critical dimension of the 3-state Potts model - Chester,SM; Su,N (Physical Review D, 2025)
We consider the 3-state Potts model in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi><a:mo>≥</a:mo><a:mn>2</a:mn></a:math> dimensions. For <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi></c:math> less than the upper critical dimension <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>d</e:mi><e:mrow><e:mi>crit</e:mi></e:mrow></e:msub></e:math>, the model has a critical and a tricritical fixed point. In <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>d</g:mi><g:mo>=</g:mo><g:mn>2</g:mn></g:math>, these fixed points are described by minimal models, and so are exactly solvable. For <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>d</i:mi><i:mo>></i:mo><i:mn>2</i:mn></i:math>, however, strong coupling makes them difficult to study and there is no consensus on the value of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>d</k:mi><k:mrow><k:mi>crit</k:mi></k:mrow></k:msub></k:math>. 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 ma