标题： 层状无序的二聚体 显示英文标题

标题： Dimers with layered disorder

摘要： 我们研究了具有淬火随机边权的正方形网格上的二聚体模型。随机性被选择为具有分层结构，类似于著名的McCoy-Wu无序伊辛模型的结构。无序具有高度非平凡的影响，并在“液体”（或“无质量”）相的一个点上产生了自由能的本质奇异性，此时二聚体-二聚体相关性的衰减为$e^{-\sqrt{{\rm distance}}}$，而在均匀二聚体模型中，此时自由能是实解析的，相关性衰减为$1/({\rm distance})^2$。此外，在均匀模型中处于从有质量（气体）相到无质量（液体）相过渡的一个点上，特征性的过渡临界指数3/2（Pokrovsky-Talapov定律）被无序修改为一个在3/2到无穷大之间连续变化的指数。 显示英文摘要

摘要： We study the dimer model on the square grid, with quenched random edge weights. Randomness is chosen to have a layered structure, similar to that of the celebrated McCoy-Wu disordered Ising model. Disorder has a highly non-trivial effect and it produces an essential singularity of the free energy, with $e^{-\sqrt{{\rm distance}}}$ decay of dimer-dimer correlations, at a point of the ``liquid'' (or ``massless'') phase where the homogeneous dimer model has instead a real analytic free energy and correlations decaying like $1/({\rm distance})^2$. Moreover, at a point where the homogeneous model has a transition between a massive (gaseous) and massless (liquid) phase, the critical exponent 3/2 (Pokrovsky-Talapov law), characteristic of the transition between the two regimes, is modified by disorder into an exponent that ranges continuously between 3/2 and infinity.