New Zealand Law
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Is the adjacent tenancy owned by the same landlord? That may help if you complain to the landlord about the other tenants, as there is an obligation to provide quiet enjoyment, which means without the noise and trouble. Otherwise to cancel the tenancy you need to first ask the landlord and if they don't agree, then you have to apply to the Tenancy Tribunal to cancel the tenancy. The grounds are that this is causing extreme hardship, so you have to explain the stress especially on your partner.
The behaviour you describe should be carefully documented and may be grounds to terminate. But try asking the landlord first and explain you think you can force the issue if they don't help.