  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.
