  Magic, or nonstabilizerness, characterizes how far away a state is from the
stabilizer states, making it an important resource in quantum computing, under
the formalism of the Gotteman-Knill theorem. In this paper, we study the magic
of the $1$-dimensional Random Matrix Product States (RMPSs) using the
$L_{1}$-norm measure. We firstly relate the $L_{1}$-norm to the $L_{4}$-norm.
We then employ a unitary $4$-design to map the $L_{4}$-norm to a $24$-component
statistical physics model. By evaluating partition functions of the model, we
obtain a lower bound on the expectation values of the $L_{1}$-norm. This bound
grows exponentially with respect to the qudit number $n$, indicating that the
$1$D RMPS is highly magical. Our numerical results confirm that the magic grows
exponentially in the qubit case.
