Question

I was wondering if there are any references on the critical exponents of the 2D XY model, and in particular, the value of η in the correlations function ⟨σ₀⋅ σᵣ⟩ at Tc (defined by the BKT transition).

Answer 1

The critical exponent η in the 2D XY model at the BKT transition is complex and requires referral to specialized literature in condensed matter physics for precise values.

Step-by-step explanation:

The value of the critical exponent η in the correlation function ⟨σ₀⋅ σᵣ⟩ for the 2D XY model at the critical temperature (BKT transition) is a subject of exacting research in condensed matter physics. While the exact value of η can be difficult to determine due to the intricacies of the XY model, the Berezinskii-Kosterlitz-Thouless (BKT) transition theory indicates that η undergoes a continuous change at the transition temperature Tc and is related to the decay of the correlation function, which aligns with expectations from topological defect driven phase transitions. For detailed numerical values and discussions about the critical exponents, including η, one would typically refer to scholarly articles and advanced textbooks on statistical mechanics or superconductivity that specialize in quantum phase transitions and the BKT transition.