597 citations · 2.2k across the 55 of their papers we have counts for
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Absence of magnetism in continuous-spin systems with long-range antialigning forces
Marek Biskup, Nicholas Crawford
We consider continuous-spin models on the -dimensional hypercubic lattice with the spins \emph{a priori} uniformly distributed over the unit sphere in (with …
True nature of long-range order in a plaquette orbital model
Marek Biskup, Roman Kotecky
We analyze the classical version of a plaquette orbital model that was recently introduced and studied numerically by S. Wenzel and W. Janke. In this model, edges of the square lat…
Reflection positivity and phase transitions in lattice spin models
Marek Biskup
Reflection positivity (RP) is a property of Gibbs measures exhibited by a class of lattice spin systems that include the Ising, Potts and Heisenberg models. The RP property is usef…
Quantum spin systems at positive temperature
Marek Biskup, Lincoln Chayes, Shannon Starr
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates…
Forbidden gap argument for phase transitions proved by means of chessboard estimates
Marek Biskup, Roman Kotecky
Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a poin…
Mean-field driven first-order phase transitions in systems with long-range interactions
Marek Biskup, Lincoln Chayes, Nicholas Crawford
We consider a class of spin systems on with vector valued spins $(\bS_x)$ that interact via the pair-potentials $J_{x,y} \bS_x\cdot\bS_y$. The interactions are generally spr…