A Monte Carlo examination of the numerical values of universal quantities in spatial dimension two

Abstract By simulating a two-dimensional dimerized spin-1/2 antiferromagnet with the quantum Monte Carlo method, the numerical values of two universal quantities associated with the quantum critical regime (QCR), namely $$S(\pi ,\pi )/\left( \chi _s T\right) $$ S ( π , π ) / χ s T and $$c/\left( T\xi \right) $$ c / T ξ , are determined. Here $$S(\pi ,\pi )$$ S ( π , π ) , $$\chi _s$$ χ s , c , $$\xi ,$$ ξ , and T are the staggered structure factor, the staggered susceptibility, the spin-wave velocity, the correlation length, and the temperature, respectively. Our calculations lead to $$S(\pi ,\pi )/\left( \chi _s T\right) \sim 1.073$$ S ( π , π ) / χ s T ∼ 1.073 and $$c/\left( T\xi \right) \sim 0.963$$ c / T ξ ∼ 0.963 , which are in better consistency with the leading theoretical predictions than those including the next-to-leading-order terms. This scenario was also observed for the Wilson ratio W and $$\chi _u c^2/T$$ χ u c 2 / T ( $$\chi _u$$ χ u is the uniform susceptibility) of QCR. The presented outcomes here and those in the literature suggest that it is desirable to conduct a refined analytic calculation to resolve the puzzle of why the inclusion of higher-order terms leads to less accurate predictions for these universal quantities. Graphical abstract $$S(\pi ,\pi ){/}\left( \chi _s T\right) $$ S ( π , π ) /