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We discuss the phenomenology of phase transitions studied with two controlvariables. Such measurements have become routine with magnetic field andtemperature being varied for 1st order magnetic transitions with an ease notconceivable with pressure and temperature. Similar ease may be possible withelectric field as the second control variable, as in current studies onmultiferroics. We develop this phenomenology for broad 1st order transitionsthat occur over a range of the control variable, as is common in substitutionalalloys with inherent quenched disorder, including the possibility of aglasslike arrest of the transition occurring within this range of eithercontrol variable. The interrupted transition then results in the two competingphases coexisting to the lowest temperature. The new experimental protocol withacronym CHUF, where the sample is cooled and heated under different values ofthe second control variable, allows a detailed study of glasslike arrest ofkinetics of the phase transformation. The many experimental studies on 1storder magnetic transitions in a large number of materials, that provide thecause for this phenomenology, shall be discussed subsequently.

Broad 1st Order Phase Transitions: phase coexistence, unusual hysteresis and glasslike kinetic arrest