Ruppeiner geometry of the 2D Ising model at three temperatures

The trust attractor sits on the col between rigid order and formless disorder

Three saddle-shaped surfaces for the ordered, critical, and disordered phases; the critical surface is steepest, with a deep valley and a sharp ridge Three saddle-shaped surfaces for the ordered, critical, and disordered phases; the critical surface is steepest, with a deep valley and a sharp ridge

Three saddle surfaces show the ordered, critical, and disordered phases of the two-dimensional Ising model. The critical surface has the deepest valley and sharpest ridge, marking high sensitivity along both plotted coordinates; the measured condition number and deviation under each panel come from the companion Ising Fisher-spectrum simulation (the critical panel reports the nearest sampled T = 2.30).