Phase Transitions for $$\phi ^4_3$$

Abstract We establish a surface order large deviation estimate for the magnetisation of low temperature $$\phi ^4_3$$ ϕ 3 4 . As byproduct, we obtain decay spectral gap its Glauber dynamics given by singular stochastic PDE. Our main technical contributions are contour bounds , which extends 2D results Glimm et al. (Commun Math Phys 45(3):203–216, 1975). adapt an argument Bodineau (J 41(3):1033–1098, 2000) to use these study phase segregation. The challenge is handle ultraviolet divergences whilst preserving structure potential. To do this, build on variational approach stability developed recently Barashkov and Gubinelli (Duke Math. J. 169(17):3339–3415, 2020).