If you don't want to receive these sorts of emails from artists, navigate to "Account" under the "ME" tab, and scroll down to the "Privacy & Notifications" section. Uncheck the boxes next to:
"Receive an email when a model sends a message to all of her fans"
"Receive an email when a model sends a message to all of her friends"
Scroll to the bottom and click on "Submit form". These options will take care of the email notifications. If you want to block an Artist from sending you any correspondence, including a Zivity message, scroll even further down to the "Ignore Fan Messages" section. Locate the Artist you do not want to receive a fan message from and click on "Ignore" next to their name.