Structures of $p$-shell double-$\mathrm{\Lambda }$ hypernuclei studied with microscopic cluster models

$0s$-orbit $\mathrm{\Lambda }$ states in $p$-shell double-$\mathrm{\Lambda }$ hypernuclei ($^{
,A}{\Lambda\Lambda}Z$),$^{\ ,8}{\Lambda\Lambda}$\text{Li}$$,$^{
,9}{\Lambda\Lambda}$\text{Li}$$,$^{10,11,12}{\ \ \ \
\Lambda\Lambda}$\text{Be}$$,$^{12,13}{\ \ \Lambda\Lambda}$\text{B}$$,and$^{,14}{\Lambda\Lambda}$\text{C}$$ are investigated. Microscopic cluster models are applied to core nuclear part and a potential model is adopted for $\mathrm{\Lambda }$ particles. The $\mathrm{\Lambda }$-core potential is a folding potential obtained with effective $G$-matrix $\mathrm{\Lambda }$-$N$ interactions, which reasonably reproduce energy spectra of ${}_{\mathrm{\Lambda }}^{A-1}Z$. System dependence of the $\mathrm{\Lambda }$-$\mathrm{\Lambda }$ binding energies is understood by the core polarization energy from nuclear size reduction. Reductions of nuclear sizes and $E2$ transition strengths by $\mathrm{\Lambda }$ particles are also discussed.