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There are two types of fundamental phenomena on universality in physics.One is the well-known universal critical phenomenon near a phase transition.The other one is universal relations governed by Contact,a central quantity to rule all dilute many-body systems.In this talk,I will discuss the intrinsic connection between these two phenomena in ultra cold atoms.Using exact thermodynamic relations,I will show that Contact exhibits a variety of critical phenomena that are uniquely determined by the universality class of the phase transition in many-body systems.These critical phenomena will be demonstrated using a prototypical exactly solvable model in one-dimensional strongly interacting fermions.