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Springer proceedings in mathematics & statistics

Meta-conformal Invariance in the Directed Glauber-Ising Chain

Stoimen Stoimenov, Malte Henkel

Published Jan 1, 2020• 3 citations
Publisher
DOI
10.1007/978-981-15-7775-8_37

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Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1 , none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.