  Upcoming multi-wavelength astronomical surveys will soon discover all massive
galaxy clusters and provide unprecedented constraints on cosmology and cluster
astrophysics. In this paper, we investigate the constraining power of the
multi-band cluster surveys, through a joint analysis of three observables
associated with clusters of galaxies, including thermal Sunyaev-Zel'dovich
(tSZ) effect in cosmic microwave background (CMB), X-ray emission of ionized
gas, and gravitational weak lensing effect of background galaxies by the
cluster's gravitational potential. We develop a theoretical framework to
predict and interpret two-point correlation statistics among the three
observables using a semi-analytic model of intracluster medium (ICM) and
halo-based approach. In this work, we show that the auto- and cross-angular
power spectra in tSZ, X-ray and lensing statistics from upcoming missions
(eROSITA, CMB-S4, and LSST) can help break the degeneracy between cosmology and
ICM physics. These correlation statistics are less sensitive to selection
biases, and are able to probe ICM physics in distant, faint and small clusters
that are otherwise difficult to be detected individually. We show that the
correlation statistics are able to provide cosmological constraints comparable
to the conventional cluster abundance measurements, while constraining cluster
astrophysics at the same time. Our results indicate that the correlation
statistics can significantly enhance the scientific returns of upcoming
multi-wavelength cluster surveys.
