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A Missing Partner Model With 24-plet Breaking SU(5)
We give a missing partner model using 24-plet instead of 75-plet to break the
SU(5) symmetry. Fermion masses and mixing are generated through the
Georgi-Jarlskog mechanism. The model is constructed at renormalizable level at
very high energy. The perturbative region is extended for the unification gauge
coupling. Constrains by proton decay is also satisfied.Comment: 18 pages, 6 figure
Complex phase diagram and supercritical matter
Supercritical region is often described as uniform with no definite
transitions. The distinct behaviors of the matter therein, e.g., as liquid-like
and gas-like, however, indicate their should-be different belongings. Here, we
provide a mathematical description of these phenomena by revisiting the
Lee-Yang (LY) theory and using a complex phase diagram, e.g. a 4-D one with
complex and . Beyond the critical point, the 2-D phase diagram with real
and , i.e. the physical plane, is free of LY zeros and hence no
criticality emerges. But off-plane zeros in this 4-D scenario still come into
play by inducing critical anomalies for different physical properties. This is
evidenced by the correlation between the Widom lines and LY edges in van der
Waals model and water. The present distinct criteria to distinguish the
supercritical matter manifest the high-dimensional feature of the phase
diagram: e.g. when the LY zeros of complex or are projected onto the
physical plane, a boundary defined by isobaric heat capacity or adiabatic
compression coefficient emanates. These results demonstrate the incipient
phase transition nature of the supercritical matter
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