FRACTIONAL EXCLUSION STATISTICS AND THE BROKEN 3RD LAW OF THERMODYNAMICS - ITS IMPLICATION TO THE CONJECTURE OF BERRYS PHASE IN CRYSTALLINEICE

The crystalline ice is known to have the 'residual entropy'' in the lo w temperature limit. We show that the residual entropy of ice may be r eformulated in terms of the fractional exclusion statistics of Haldane at T = 0 with the statistical interaction parameter alpha = 0.867. In other words, the fractional exclusion at T = 0 implies the broken thi rd law of thermodynamics. Then the question arises whether the chemist ry-driven fractional exclusion statistics in ice has anything to do wi th the topology-driven anyon (fractional phase) statistics as in the c ase of the quasi-particles in FQHE. In the present study, we perform e lectronic structure calculations for ice in order to probe the Born-Op penheimer energy surface. We find the possibility that there exist Ber ry's phase contributing to the residual entropy (macroscopic ground-st ate degeneracy), establishing the connection between the fractional ex clusion and the fractional phase.