Infinite cascades of phase transitions in the classical Ising chain.We report exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field.  We propose a duality transformation which maps the Ising chain onto the m-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs.  Then the m-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the m-leg tube.  We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in m-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.
Ising
Infinite cascades of phase transitions in the classical Ising chain.We report exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field.  We propose a duality transformation which maps the Ising chain onto the m-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs.  Then the m-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the m-leg tube.  We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in m-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.
Ising