Multicritical pinch-offs on the Triangular and Kagome lattice

Multicritical points are extremely difficult to pinpoint and study numerically owing to the large correlation lengths and sensitive dependence of multicritical exponents on parameter values. We study the experimentally accessible problem of the frustrated triangular lattice Ising antiferromagnet with ferromagnetic second and third nearest neighbours using highly efficient Monte-Carlo worm algorithms. We show that the width in temperature of the two-step melting transition of the three-sublattice ordered phase stabilised by ferromagnetic second-nearest neighbours can be tuned by the strength of the third-nearest neighbour ferromagnetic interactions. Increasing third-nearest neighbour ferromagnetic interactions causes the two-step melting phase to pinch-off into a multicritical point. Further increase in the third-nearest neighbour interactions makes the melting weakly first-ordered. We are able to numerically pinpoint the location of the multicritical point and calculate multicritical exponents to show that this multicritical point belongs to the universality class of a Z6 parafermionic CFT. We extend our analysis to the frustrated Kagome Ising antiferromagnet wherein a similar two-step melting of the three-sublattice ordered phase can be tuned into a multicritical pinch-off.