Residual entropy of spin-s triangular Ising antiferromagnet

We employ a thermodynamic integration method (TIM) to establish the values of the residual entropy for the geometrically frustrated spin-s triangular Ising antiferromagnet, with the spin values s = 1/2, 1, 3/2, 2 and 5/2. The case of s = 1/2, for which the exact value is known, is used to assess the TIM performance. We also obtain an analytical formula for the lower bound in a general spin-s model and conjecture that it should reasonably approximate the true residual entropy for sufficiently large $s$. Implications of the present results in relation to reliability of the TIM as an indirect method for calculating global thermodynamic quantities, such as the free energy and the entropy, in similar systems involving frustration and/or higher spin values by standard Monte Carlo sampling are briefly discussed.