  Elastic constants, thermal expansion, magnetostriction and heat capacity
measurements were performed with and without applied magnetic field on a single
crystal of UIrSi$_3$. The elastic properties were interpreted within the theory
of the strain-exchange effect. The exchange-striction model together with the
Ising model for the behavior of magnetic localized 5$f$ electrons and itinerant
electrons of uranium correctly reproduces the main features of our
magneto-acoustic experiments in UIrSi$_3$. Data on thermal expansion and
magnetostriction confirm the conclusion that the dominant contribution of the
measured temperature and field change in the speed of sound comes from the
change in the elastic modulus itself. Based on the analysis of heat capacity
measurements in the magnetic field, we explain the significant anomalies at the
second-order branch of the phase transition boundary as a manifestation of the
tricritical fluctuations, dominating the region below the tricritical point.
The outcome confirms the 3D Ising model, at zero and low magnetic fields, with
a crossover to the mean-field tricritical behavior at fields close to the
tricritical point, where tricritical fluctuations dominate the temperature
evolution of the given property.
