First Rental - Early Lease Termination by Tenant in AZ

[Margaret Loper]

Our first tenant gave a 30 day notice to move out after staying in the home for 4 months on a year lease. It took us about a month and a half to secure another tenant after tenant moved out. There is no provision in the lease that says that they can break the lease with a 30 day notice. We deducted unpaid rent up to the day the other tenants signed a new lease and refunded what was remaining, which is next to nothing. Is this wrong in any way?