Title: Critical and geometric properties of magnetic polymers across the globule-coil transition

Abstract: We study a lattice model of a magnetic elastomer, where Ising spins are located on the sites of a lattice self-avoiding walk in $d=2$. We consider the regime where both conformations and magnetic degrees of freedom are dynamic, thus the Ising model is defined on a dynamic lattice and conformations generate an annealed disorder. We perform Monte Carlo simulations across the theta-point and find the joint ferromagnet-to-paramagnet and globule-coil transition, which is continuous -- in contrast to $d=3$ where it is first-order. At the transition, the metric exponent takes the theta-polymer value, but the crossover exponent is different.