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• W4220831763 abstract "Abstract We establish a surface order large deviation estimate for the magnetisation of low temperature $$phi ^4_3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> . As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics given by the $$phi ^4_3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> singular stochastic PDE. Our main technical contributions are contour bounds for $$phi ^4_3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> , which extends 2D results by Glimm et al. (Commun Math Phys 45(3):203–216, 1975). We adapt an argument by Bodineau et al. (J Math Phys 41(3):1033–1098, 2000) to use these contour bounds to study phase segregation. The main challenge to obtain the contour bounds is to handle the ultraviolet divergences of $$phi ^4_3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> whilst preserving the structure of the low temperature potential. To do this, we build on the variational approach to ultraviolet stability for $$phi ^4_3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> developed recently by Barashkov and Gubinelli (Duke Math. J. 169(17):3339–3415, 2020)." @default.
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• W4220831763 date "2022-03-30" @default.
• W4220831763 modified "2023-09-26" @default.
• W4220831763 title "Phase Transitions for $$phi ^4_3$$" @default.
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• W4220831763 doi "https://doi.org/10.1007/s00220-022-04353-6" @default.
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