



01603nas a2200145   4500008004100000245010500041210006900146260001400215520111300229100002901342700001501371700001901386700001501405856003701420       2020                        eng d00aDistinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives0 aDistinct Critical Behaviors from the Same State in Quantum Spin   c9/10/20203 a<p>There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.&nbsp;</p>1 aBaldwin, Christopher, L.1 aShivam, S.1 aSondhi, S., L.1 aKardar, M.  uhttps://arxiv.org/abs/2009.05064