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We examine the discontinuous first-order superfluid $^3$He A to B transitionin the vicinity of the polycritical point (2.232 mK and 21.22 bar). We findpath-dependent transitions: cooling at fixed pressure yields a well definedtransition line in the temperature-pressure plane, but this line can bereliably crossed by depressurizing at nearly constant temperature aftertransiting $T_{\rm c}$ at a higher pressure. This path dependence is notconsistent with any of the standard B-phase nucleation mechanisms in theliterature. This symmetry breaking transition is a potential simulator forfirst order transitions in the early universe.

Path-Dependent Supercooling of the $^3$He Superfluid A-B transition